Obstructions to matricial stability of discrete groups and almost flat K-theory

Autor:	Dadarlat, Marius
Rok vydání:	2020
Předmět:	Mathematics - Operator Algebras Mathematics - Group Theory Mathematics - K-Theory and Homology
Druh dokumentu:	Working Paper
Popis:	A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that matricial stability implies the vanishing of the rational cohomology of G in all nonzero even dimensions. We revisit a method of constructing almost flat K-theory classes of BG which involves the dual assembly map and quasidiagonality properties of G. The existence of almost flat K-theory classes of BG which are not flat represents an obstruction to matricial stability of G due to continuity properties of the approximate monodromy correspondence. Comment: Minor revision, to appear in Adv. Math
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.12655 Zobrazit plný text záznamu View this record from Arxiv