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006 m     o  d        
007 cr cnu||||||||
008 160801s2015    sz      ob    001 0 eng d
020   $a9783319193335
035   $ab1430577x-39ule_inst
040   $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng
082 04$a512
084   $aAMS 20F65
084   $aAMS 03C20
084   $aAMS 03C65
084   $aAMS 37A15
084   $aLC QA174.2.C37
100 1 $aCapraro, Valerio$0717976
245 10$aIntroduction to sofic and hyperlinear groups and connes' embedding conjecture$h[e-book] /$cValerio Capraro, Martino Lupini ; with an appendix by Vladimir Pestov
260   $aCham [Switzerland] :$bSpringer,$c2015
300   $a1 online resource (viii, 151 pages)
440  0$aLecture Notes in Mathematics,$x1617-9692 ;$v2136
504   $aIncludes bibliographical references and index
505 0 $aIntroduction ; Sofic and hyperlinear groups ; Connes' embedding conjecture ; Conclusions
520   $aThis monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems. Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups. The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present
650  0$aGroup theory
650  0$aOperator theory
700 1 $aLupini, Martino$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0721405
856 40$uhttp://link.springer.com/book/10.1007/978-3-319-19333-5$zAn electronic book accessible through the World Wide Web
907   $a.b1430577x$b03-03-22$c01-08-16
912   $a991003265709707536
996   $aIntroduction to sofic and hyperlinear groups and Connes' embedding conjecture$91413246
997   $aUNISALENTO
998   $ale013$b01-08-16$cm$d@  $e-$feng$gsz $h0$i0