TeX files

Tensorially absorbing inclusions/letterfonts.tex

@@ -0,0 +1,77 @@
+%commands
+\newcommand{\ms}{\mathscr}
+\newcommand{\mc}{\mathcal}
+\newcommand{\mf}{\mathfrak}
+\newcommand{\nin}{\not\in}
+\newcommand{\bs}{\backslash}
+\newcommand{\nsg}{\unlhd}
+\newcommand{\ov}{\overline}
+%blackboard
+\newcommand{\bN}{\mathbb{N}}
+\newcommand{\bR}{\mathbb{R}}
+\newcommand{\bZ}{\mathbb{Z}}
+\newcommand{\bQ}{\mathbb{Q}}
+\newcommand{\bF}{\mathbb{F}}
+\newcommand{\bK}{\mathbb{K}}
+\newcommand{\bG}{\mathbb{G}}
+\newcommand{\bE}{\mathbb{E}}
+\newcommand{\bC}{\mathbb{C}}
+\newcommand{\bV}{\mathbb{V}}
+\newcommand{\bA}{\mathbb{A}}
+\newcommand{\bP}{\mathbb{P}}
+\newcommand{\bD}{\mathbb{D}}
+\newcommand{\bT}{\mathbb{T}}
+\newcommand{\bM}{\mathbb{M}}
+\newcommand{\bB}{\mathbb{B}}
+\newcommand{\bL}{\mathbb{L}}
+\newcommand{\bX}{\mathbb{X}}
+\newcommand{\bY}{\mathbb{Y}}
+\newcommand{\1}{{\bf 1}}
+\newcommand{\0}{{\bf 0}}
+
+%mathcal
+\newcommand{\cM}{\mathcal{M}}
+\newcommand{\cN}{\mathcal{N}}
+\newcommand{\cC}{\mathcal{C}}
+\newcommand{\cB}{\mathcal{B}}
+\newcommand{\cS}{\mathcal{S}}
+\newcommand{\cI}{\mathcal{I}}
+\newcommand{\cO}{\mathcal{O}}
+\newcommand{\cP}{\mathcal{P}}
+\newcommand{\cA}{\mathcal{A}}
+\newcommand{\cL}{\mathcal{L}}
+\newcommand{\cF}{\mathcal{F}}
+\newcommand{\cH}{\mathcal{H}}
+\newcommand{\cK}{\mathcal{K}}
+\newcommand{\cD}{\mathcal{D}}
+\newcommand{\cE}{\mathcal{E}}
+\newcommand{\cT}{\mathcal{T}}
+\newcommand{\cZ}{\mathcal{Z}}
+\newcommand{\cU}{\mathcal{U}}
+\newcommand{\cJ}{\mathcal{J}}
+\newcommand{\cG}{\mathcal{G}}
+\newcommand{\cR}{\mathcal{R}}
+\newcommand{\cQ}{\mathcal{Q}}
+\newcommand{\cY}{\mathcal{Y}}
+%terns
+\newcommand{\bh}{\mathcal{B}(\mathcal{H})}
+\newcommand{\bk}{\mathcal{B}(\mathcal{K})}
+\newcommand{\kh}{\mathcal{K}(\mathcal{H})}
+\newcommand{\fh}{\mathcal{F}(\mathcal{H})}
+\newcommand{\sa}{\mathcal{S}(\mathcal{A})}
+\newcommand{\bx}{\mathcal{B}(\mathbb{X}}
+\newcommand{\by}{\mathcal{C}(\mathbb{Y}}
+
+%frak
+\newcommand{\fX}{\mathfrak{X}}
+\newcommand{\fS}{\mathfrak{S}}
+\newcommand{\fM}{\mathfrak{M}}
+\newcommand{\fN}{\mathfrak{N}}
+\newcommand{\fF}{\mathfrak{F}}
+\newcommand{\fJ}{\mathfrak{J}}
+\newcommand{\fT}{\mathfrak{T}}
+\newcommand{\fA}{\mathfrak{A}}
+\newcommand{\fB}{\mathfrak{B}}
+\newcommand{\fP}{\mathfrak{P}}
+\newcommand{\fQ}{\mathfrak{Q}}
+\newcommand{\fO}{\mathfrak{O}}

Tensorially absorbing inclusions/macros.tex

@@ -0,0 +1,104 @@
+% tensor products
+\newcommand{\thk}{\cH\otimes\cK}
+\newcommand{\amb}{\bA \otimes_{\max} \bB}
+\newcommand{\omax}{\otimes_{\max}}
+\newcommand{\omin}{\otimes_{\min}}
+\newcommand{\ovn}{\overline{\otimes}}
+
+% probability
+\newcommand{\PS}{(\Omega,\cM,\cP)}
+\newcommand{\rvf}{f:\Omega \to \bR}
+\newcommand{\linf}{\cL^{\infty -}\PS}
+\newcommand{\probc}{\text{Prob}_c(\bR)}
+\newcommand{\prob}{\text{Prob}(\bR)}
+
+% maps
+\newcommand{\into}{\hookrightarrow}
+\newcommand{\onto}{\twoheadrightarrow}
+\newcommand{\act}{\curvearrowright}
+
+\newcommand{\ee}{\varepsilon}
+\newcommand{\sm}{\setminus}
+\newcommand{\Om}{\Omega}
+\newcommand{\simi}{\sim_{\infty}}
+
+%limits
+\newcommand{\limsupn}{\underset{n}{\text{limsup}}}
+\newcommand{\sotc}{\stackrel{\text{SOT}}{\to}}
+\newcommand{\wotc}{\stackrel{\text{WOT}}{\to}}
+\newcommand{\sotlim}{\text{SOT-}\lim}
+\newcommand{\wotlim}{\text{WOT-}\lim}
+
+% useful for nuclear, lifting maps, etc....
+\newcommand{\tphi}{\tilde{\phi}}
+\newcommand{\tpsi}{\tilde{\psi}}
+\newcommand{\hphi}{\hat{\phi}}
+\newcommand{\hpsi}{\hat{\psi}}
+\newcommand{\phil}{\phi_\lambda}
+\newcommand{\psil}{\psi_\lambda}
+\newcommand{\mkl}{M_{k(\lambda)}}
+\newcommand{\mkn}{M_{k(n)}}
+\newcommand{\phin}{\phi_n}
+\newcommand{\psin}{\psi_n}
+\newcommand{\vphi}{\varphi}
+
+\newcommand{\floor}[1]{\lfloor #1 \rfloor}
+
+\newcommand{\supp}{\text{supp}}
+\newcommand{\wk}{\text{wk}}
+\newcommand{\Tr}{\text{Tr}}
+\newcommand{\dist}{\text{dist}}
+\newcommand{\rank}{\text{rank}}
+\newcommand{\sgn}{\text{sgn}}
+
+\newcommand{\ev}{\text{ev}}
+\newcommand{\spr}{\text{spr}}
+\newcommand{\tD}{\tilde{\Delta}}
+\newcommand{\uv}{\underline}
+\newcommand{\tr}{\text{tr}}
+\newcommand{\id}{\text{id}}
+\newcommand{\ad}{\text{ad}}
+\newcommand{\Ad}{\text{Ad}}
+
+\newcommand*{\tc}[2]{(\ov{#1}^{#2},#2)}
+
+% Types for von Neumann algebras
+\newcommand{\I}{\text{I}}
+\newcommand{\II}{\text{II}}
+\newcommand{\III}{\text{III}}
+\newcommand{\IIIl}{\text{III}_{\lambda}}
+% note the last character of this last one is an "ell", its just that my font has capital i and lower-case l being the same character.....
+
+
+%operators
+% basic algebra
+\DeclareMathOperator{\Ann}{Ann}
+\DeclareMathOperator{\Hom}{Hom}
+\DeclareMathOperator{\End}{End}
+\DeclareMathOperator{\Aut}{Aut}
+\DeclareMathOperator{\im}{im}
+
+% K-theory and regularity for C*-algebras
+\DeclareMathOperator{\Ell}{Ell}
+\DeclareMathOperator{\Aff}{Aff}
+\DeclareMathOperator{\KT}{KT}
+\DeclareMathOperator{\Cu}{Cu}
+\DeclareMathOperator{\Ka}{K^{\text{alg}}}
+\DeclareMathOperator{\Ku}{K^u}
+\DeclareMathOperator{\hKa}{\ov{K}_1^{\text{alg}}}
+\DeclareMathOperator{\hku}{\ov{K}_1^u}
+
+% exponential rank and length for C*-algebras
+\newcommand{\cer}{\text{cer}}
+\newcommand{\cel}{\text{cel}}
+
+% KK-theory and Ext
+\DeclareMathOperator{\KK}{KK}
+\DeclareMathOperator{\KKn}{KK_{\text{nuc}}}
+\DeclareMathOperator{\KKs}{KK_{\text{sep}}}
+\DeclareMathOperator{\Ext}{Ext}
+\DeclareMathOperator{\Extn}{Ext_{\text{nuc}}}
+
+% direct/inverse limits
+\newcommand{\dlim}{\underset{\to}{\lim}}
+\newcommand{\ilim}{\underset{\leftarrow}{\lim}}

Tensorially absorbing inclusions/preabmle.tex

@@ -0,0 +1,52 @@
+% change this depending on what you're doing.
+%\documentclass[11pt]{amsart}
+
+%packages
+%\usepackage[margin=1.5in]{geometry}
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
+\usepackage[pdftex]{graphicx}
+\usepackage{tikz-cd}
+\usepackage{blindtext}
+
+\usepackage{hyperref,xcolor}
+\usepackage{amsmath,amsfonts,amssymb,amsthm,color,mathtools,enumitem}
+\usepackage{epstopdf}
+\usepackage{polynom}
+\usepackage{babel}
+\usepackage{mathrsfs}
+\usepackage{chngcntr}
+\usepackage{verbatim}
+\usepackage{hyphenat}
+ 
+
+\hypersetup{
+	colorlinks=true,
+	linkcolor=blue,
+	citecolor=cyan,
+	urlcolor=cyan}
+
+  %theorems
+\newtheorem{theorem}{Theorem}[section]
+\newtheorem{defn}[theorem]{Definition}
+\newtheorem{prop}[theorem]{Proposition}
+\newtheorem{cor}[theorem]{Corollary}
+\newtheorem{lemma}[theorem]{Lemma}
+\newtheorem{example}[theorem]{Example}
+\newtheorem{remark}[theorem]{Remark}
+
+\newtheorem*{resultA}{Theorem A}
+\newtheorem*{resultB}{Theorem B}
+\newtheorem*{resultC}{Theorem C}
+\newtheorem*{resultD}{Theorem D}
+\newtheorem*{resultE}{Theorem E}
+\newtheorem*{resultF}{Theorem F}
+
+%\newtheorem{result}{Theorem}[chapter]
+\newtheorem{result}{Theorem}
+%\renewcommand*{\theresult}{\arabic{chapter}.\Alph{result}}
+\renewcommand*{\theresult}{\Alph{result}}
+\newtheorem{resultcor}[result]{Corollary}
+
+\numberwithin{equation}{section}
+

Tensorially absorbing inclusions/tensorially_absorbing_inclusions.bbl

@@ -0,0 +1,288 @@
+\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
+\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
+% \MRhref is called by the amsart/book/proc definition of \MR.
+\providecommand{\MRhref}[2]{%
+  \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
+}
+\providecommand{\href}[2]{#2}
+\begin{thebibliography}{BGSW22}
+
+\bibitem[AGJP22]{AGJP22}
+Massoud Amini, Nasser Golestani, Saeid Jamali, and N.~Christopher Phillips,
+  \emph{Group actions on simple tracially $\mathcal{Z}$-absorbing
+  {C}*-algebras}, arXiv preprint arXiv:2204.03615 (2022).
+
+\bibitem[BGSW22]{BGSW22}
+Joan Bosa, James Gabe, Aidan Sims, and Stuart White, \emph{The nuclear
+  dimension of $\mathcal{O}_\infty$-stable {C}*-algebras}, Adv. Math.
+  \textbf{401} (2022), Paper No. 108250, 51. \MR{4392219}
+
+\bibitem[Bis90]{Bisch90}
+Dietmar~H. Bisch, \emph{On the existence of central sequences in subfactors},
+  Trans. Amer. Math. Soc. \textbf{321} (1990), no.~1, 117--128. \MR{1005075}
+
+\bibitem[Bis94]{Bisch94}
+\bysame, \emph{Central sequences in subfactors. {II}}, Proc. Amer. Math. Soc.
+  \textbf{121} (1994), no.~3, 725--731. \MR{1209417}
+
+\bibitem[BO08]{BrownOzawa}
+Nathanial~P. Brown and Narutaka Ozawa, \emph{{C}*-algebras and
+  finite-dimensional approximations}, Graduate Studies in Mathematics, vol.~88,
+  American Mathematical Society, Providence, RI, 2008. \MR{2391387}
+
+\bibitem[BSKR93]{BSKR93}
+Ola Bratteli, Erling St{\o}rmer, Akitaka Kishimoto, and Mikael R{\o}rdam,
+  \emph{The crossed product of a {UHF} algebra by a shift}, Ergodic Theory
+  Dynam. Systems \textbf{13} (1993), no.~4, 615--626. \MR{1257025}
+
+\bibitem[Bur10]{Burstein10}
+Richard~D. Burstein, \emph{Commuting square subfactors and central sequences},
+  Internat. J. Math. \textbf{21} (2010), no.~1, 117--131. \MR{2642989}
+
+\bibitem[Con75]{Connes75}
+Alain Connes, \emph{Classification of automorphisms of hyperfinite factors of
+  type {II}$_1$ and {II}$_{\infty}$ and application to type {III} factors},
+  Bull. Amer. Math. Soc. \textbf{81} (1975), no.~6, 1090--1092. \MR{388117}
+
+\bibitem[Con76]{Connes76}
+\bysame, \emph{Classification of injective factors cases {II}$_1$,
+  {II}$_\infty$, {III}$_\lambda$, $\lambda \neq 1$}, Ann. of Math. (2)
+  \textbf{104} (1976), no.~1, 73--115. \MR{454659}
+
+\bibitem[CS19]{CameronSmith19}
+Jan Cameron and Roger~R. Smith, \emph{A {G}alois correspondence for reduced
+  crossed products of simple {C}*-algebras by discrete groups}, Canad. J. Math.
+  \textbf{71} (2019), no.~5, 1103--1125. \MR{4010423}
+
+\bibitem[Cun77]{Cuntz77}
+Joachim Cuntz, \emph{Simple {C}*-algebras generated by isometries}, Comm. Math.
+  Phys. \textbf{57} (1977), no.~2, 173--185. \MR{467330}
+
+\bibitem[Dav96]{DavidsonBook1}
+Kenneth~R. Davidson, \emph{{C}*-algebras by example}, Fields Institute
+  Monographs, vol.~6, American Mathematical Society, Providence, RI, 1996.
+  \MR{1402012}
+
+\bibitem[DW09]{DadarlatWinter09}
+Marius Dadarlat and Wilhelm Winter, \emph{On the {KK}-theory of strongly
+  self-absorbing {C}*-algebras}, Math. Scand. \textbf{104} (2009), no.~1,
+  95--107. \MR{2498373}
+
+\bibitem[ER21]{EchterhoffRordam21}
+Siegfried Echterhoff and Mikael R{\o}rdam, \emph{Inclusions of {C}*-algebras
+  arising from fixed-point algebras}, arXiv preprint arXiv:2108.08832 (2021).
+
+\bibitem[EST23]{EndersSchemaitatTikuisis23}
+Dominic Enders, Andr{\'e} Schemaitat, and Aaron Tikuisis, \emph{Corrigendum to
+  ``{$K$}-theoretic characterization of {C}*-algebras with approximately inner
+  flip''}, arXiv preprint arXiv:2303.11106 (2023).
+
+\bibitem[EV00]{ElliottVilladsen00}
+George~A. Elliott and Jesper Villadsen, \emph{Perforated ordered
+  {$K_0$}-groups}, Canad. J. Math. \textbf{52} (2000), no.~6, 1164--1191.
+  \MR{1794301}
+
+\bibitem[Gab19]{Gabe19}
+James Gabe, \emph{Classification of $\mathcal{O}_\infty$-stable {C}*-algebras},
+  arXiv preprint arXiv:1910.06504 (2019).
+
+\bibitem[Gab20]{Gabe20}
+\bysame, \emph{A new proof of {K}irchberg's $\mathcal{O}_2$-stable
+  classification}, J. Reine Angew. Math. \textbf{761} (2020), 247--289.
+  \MR{4080250}
+
+\bibitem[GH18]{GardellaHirshberg18}
+Eusebio Gardella and Ilan Hirshberg, \emph{Strongly outer actions of amenable
+  groups on $\mathcal{Z}$-stable {C}*-algebras}, arXiv preprint
+  arXiv:1811.00447 (2018).
+
+\bibitem[HO13]{HirshbergOrovitz13}
+Ilan Hirshberg and Joav Orovitz, \emph{Tracially $\mathcal{Z}$-absorbing
+  {C}*-algebras}, J. Funct. Anal. \textbf{265} (2013), no.~5, 765--785.
+  \MR{3063095}
+
+\bibitem[HRW07]{HirshbergRordamWinter07}
+Ilan Hirshberg, Mikael R{\o}rdam, and Wilhelm Winter,
+  \emph{$\mathcal{C}_0({X})$-algebras, stability and strongly self-absorbing
+  {C}*-algebras}, Math. Ann. \textbf{339} (2007), no.~3, 695--732. \MR{2336064}
+
+\bibitem[HW41]{HurewiczWallman}
+Witold Hurewicz and Henry Wallman, \emph{Dimension theory}, Princeton
+  Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J.,
+  1941. \MR{0006493}
+
+\bibitem[HW07]{HirshbergWinter07}
+Ilan Hirshberg and Wilhelm Winter, \emph{{R}okhlin actions and self-absorbing
+  {C}*-algebras}, Pacific J. Math. \textbf{233} (2007), no.~1, 125--143.
+  \MR{2366371}
+
+\bibitem[Izu02]{Izumi02}
+Masaki Izumi, \emph{Inclusions of simple {C}*-algebras}, J. Reine Angew. Math.
+  \textbf{547} (2002), 97--138.
+
+\bibitem[Izu04]{Izumi04}
+\bysame, \emph{Finite group actions on {C}*-algebras with the {R}ohlin
+  property. {I}}, Duke Math. J. \textbf{122} (2004), no.~2, 233--280.
+  \MR{2053753}
+
+\bibitem[JS99]{JiangSu99}
+Xinhui Jiang and Hongbing Su, \emph{On a simple unital projectionless
+  {C}*-algebra}, Amer. J. Math. \textbf{121} (1999), no.~2, 359--413.
+  \MR{1680321}
+
+\bibitem[Kaw99]{Kawamuro99}
+Keiko Kawamuro, \emph{Central sequence subfactors and double commutant
+  properties}, Internat. J. Math. \textbf{10} (1999), no.~1, 53--77.
+  \MR{1678538}
+
+\bibitem[Kir06]{Kirchberg06}
+Eberhard Kirchberg, \emph{Central sequences in {C}*-algebras and strongly
+  purely infinite algebras}, Operator {A}lgebras: {T}he {A}bel {S}ymposium
+  2004, Abel Symp., vol.~1, Springer, Berlin, 2006, pp.~175--231. \MR{2265050}
+
+\bibitem[KP00]{KirchbergPhillips00}
+Eberhard Kirchberg and N.~Christopher Phillips, \emph{Embedding of exact
+  {C}*-algebras in the {C}untz algebra $\mathcal{O}_2$}, J. Reine Angew. Math.
+  \textbf{525} (2000), 17--53. \MR{1780426}
+
+\bibitem[McD69]{McDuff69}
+Dusa McDuff, \emph{Uncountably many {II}$_1$ factors}, Ann. of Math. (2)
+  \textbf{90} (1969), 372--377. \MR{259625}
+
+\bibitem[Mor09]{deLacerdaMortari09}
+Fernando de~Lacerda Mortari, \emph{Tracial state spaces of higher stable rank
+  simple {C}*-algebras}, ProQuest LLC, Ann Arbor, MI, 2009, Thesis
+  (Ph.D.)--University of Toronto (Canada). \MR{2753146}
+
+\bibitem[MS12]{MatuiSato12}
+Hiroki Matui and Yasuhiko Sato, \emph{Strict comparison and
+  $\mathcal{Z}$-absorption of nuclear {C}*-algebras}, Acta Math. \textbf{209}
+  (2012), no.~1, 179--196. \MR{2979512}
+
+\bibitem[MvN43]{MvNIV}
+Francis~J. Murray and John von Neumann, \emph{On rings of operators. {IV}},
+  Ann. of Math. (2) \textbf{44} (1943), 716--808. \MR{9096}
+
+\bibitem[OT18]{OsakaTeruya18}
+Hiroyuki Osaka and Tamotsu Teruya, \emph{The {J}iang--{S}u absorption for
+  inclusions of unital {C}*-algebras}, Canad. J. Math. \textbf{70} (2018),
+  no.~2, 400--425. \MR{3759005}
+
+\bibitem[Pop89]{Popa89}
+Sorin Popa, \emph{Sousfacteurs, actions des groupes et cohomologie}, C. R.
+  Acad. Sci. Paris S\'{e}r. I Math. \textbf{309} (1989), no.~12, 771--776.
+  \MR{1054961}
+
+\bibitem[Pop00]{Popa00}
+\bysame, \emph{On the relative {D}ixmier property for inclusions of
+  {C}*-algebras}, J. Funct. Anal. \textbf{171} (2000), no.~1, 139--154.
+  \MR{1742862}
+
+\bibitem[Rae05]{RaeburnBook}
+Iain Raeburn, \emph{Graph algebras}, CBMS Regional Conference Series in
+  Mathematics, vol. 103, Published for the Conference Board of the Mathematical
+  Sciences, Washington, DC; by the American Mathematical Society, Providence,
+  RI, 2005. \MR{2135030}
+
+\bibitem[R{\o}r91]{Rordam91}
+Mikael R{\o}rdam, \emph{On the structure of simple {C}*-algebras tensored with
+  a {UHF}-algebra}, J. Funct. Anal. \textbf{100} (1991), no.~1, 1--17.
+  \MR{1124289}
+
+\bibitem[R{\o}r92]{Rordam92}
+\bysame, \emph{On the structure of simple {C}*-algebras tensored with a
+  {UHF}-algebra. {II}}, J. Funct. Anal. \textbf{107} (1992), no.~2, 255--269.
+  \MR{1172023}
+
+\bibitem[R{\o}r95]{Rordam95}
+\bysame, \emph{Classification of certain infinite simple {C}*-algebras}, J.
+  Funct. Anal. \textbf{131} (1995), no.~2, 415--458. \MR{1345038}
+
+\bibitem[R{\o}r02]{RordamBook}
+\bysame, \emph{Classification of nuclear, simple {C}*-algebras}, Classification
+  of nuclear {C}*-algebras. {E}ntropy in operator algebras, Encyclopaedia Math.
+  Sci., vol. 126, Springer, Berlin, 2002, pp.~1--145. \MR{1878882}
+
+\bibitem[R{\o}r04]{Rordam04}
+\bysame, \emph{The stable and the real rank of $\mathcal{Z}$-absorbing
+  {C}*-algebras}, Internat. J. Math. \textbf{15} (2004), no.~10, 1065--1084.
+  \MR{2106263}
+
+\bibitem[R{\o}r21]{Rordam21}
+\bysame, \emph{Irreducible inclusions of simple {C}*-algebras}, arXiv preprint
+  arXiv:2105.11899 (2021).
+
+\bibitem[RS87]{RosenbergSchochet87}
+Jonathan Rosenberg and Claude Schochet, \emph{The {K}\"{u}nneth theorem and the
+  universal coefficient theorem for {K}asparov's generalized {$K$}-functor},
+  Duke Math. J. \textbf{55} (1987), no.~2, 431--474. \MR{894590}
+
+\bibitem[RW10]{RordamWinter10}
+Mikael R{\o}rdam and Wilhelm Winter, \emph{The {J}iang-{S}u algebra revisited},
+  J. Reine Angew. Math. \textbf{642} (2010), 129--155. \MR{2658184}
+
+\bibitem[Sat10]{Sato10}
+Yasuhiko Sato, \emph{The {R}ohlin property for automorphisms of the
+  {J}iang-{S}u algebra}, J. Funct. Anal. \textbf{259} (2010), no.~2, 453--476.
+  \MR{2644109}
+
+\bibitem[Sch20]{Schafhauser20}
+Christopher Schafhauser, \emph{Subalgebras of simple {AF}-algebras}, Ann. of
+  Math. (2) \textbf{192} (2020), no.~2, 309--352. \MR{4151079}
+
+\bibitem[Sch22]{Schemaitat22}
+Andr\'{e} Schemaitat, \emph{The {J}iang-{S}u algebra is strongly self-absorbing
+  revisited}, J. Funct. Anal. \textbf{282} (2022), no.~6, Paper No. 109347, 39.
+  \MR{4360358}
+
+\bibitem[Tik12]{Tikuisis12}
+Aaron Tikuisis, \emph{Regularity for stably projectionless, simple
+  {C}*-algebras}, J. Funct. Anal. \textbf{263} (2012), no.~5, 1382--1407.
+  \MR{2943734}
+
+\bibitem[Tik16]{Tikuisis16}
+\bysame, \emph{{K}-theoretic characterization of {C}*-algebras with
+  approximately inner flip}, Int. Math. Res. Not. IMRN (2016), no.~18,
+  5670--5694. \MR{3567256}
+
+\bibitem[Tom05]{Toms05}
+Andrew~S. Toms, \emph{On the independence of {$K$}-theory and stable rank for
+  simple {C}*-algebras}, J. Reine Angew. Math. \textbf{578} (2005), 185--199.
+  \MR{2113894}
+
+\bibitem[Tom08a]{Toms08b}
+\bysame, \emph{An infinite family of non-isomorphic {C}*-algebras with
+  identical {$K$}-theory}, Trans. Amer. Math. Soc. \textbf{360} (2008), no.~10,
+  5343--5354. \MR{2415076}
+
+\bibitem[Tom08b]{Toms08}
+\bysame, \emph{On the classification problem for nuclear {C}*-algebras}, Ann.
+  of Math. (2) \textbf{167} (2008), no.~3, 1029--1044. \MR{2415391}
+
+\bibitem[TW07]{TomsWinter07}
+Andrew~S. Toms and Wilhelm Winter, \emph{Strongly self-absorbing
+  {C}*-algebras}, Trans. Amer. Math. Soc. \textbf{359} (2007), no.~8,
+  3999--4029. \MR{2302521}
+
+\bibitem[TW08]{TomsWinter08}
+\bysame, \emph{{$\mathcal{Z}$}-stable {ASH} algebras}, Canad. J. Math.
+  \textbf{60} (2008), no.~3, 703--720. \MR{2414961}
+
+\bibitem[TW09]{TomsWinter09}
+\bysame, \emph{The {E}lliott conjecture for {V}illadsen algebras of the first
+  type}, J. Funct. Anal. \textbf{256} (2009), no.~5, 1311--1340. \MR{2490221}
+
+\bibitem[TWW15]{TomsWhiteWinter15}
+Andrew~S. Toms, Stuart White, and Wilhelm Winter, \emph{$\mathcal{Z}$-stability
+  and finite-dimensional tracial boundaries}, Int. Math. Res. Not. IMRN (2015),
+  no.~10, 2702--2727. \MR{3352253}
+
+\bibitem[Vil98]{Villadsen98}
+Jesper Villadsen, \emph{Simple {C}*-algebras with perforation}, J. Funct. Anal.
+  \textbf{154} (1998), no.~1, 110--116. \MR{1616504}
+
+\bibitem[Vil99]{Villadsen99}
+\bysame, \emph{On the stable rank of simple {C}*-algebras}, J. Amer. Math. Soc.
+  \textbf{12} (1999), no.~4, 1091--1102. \MR{1691013}
+
+\end{thebibliography}