2018/12/04 by Alessandro Vignati, Vignati, Alessandro
Mathematics · #03E50 #46L05 #46L40 #54D80 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Operator Algebras (math.OA) #math.GN #math.LO #math.OA #msc:03E50 #msc:46L05 #msc:46L40 #msc:54D80
paper · pdf · doi:10.48550/arxiv.1812.01306
47 pages, to appear in Annales Scientifiques de l'École Normale Supérieure (ASENS)
arxiv created 2021/05/26 · arxiv updated 2021/05/27
We prove several rigidity results for corona C^*-algebras and Čech-Stone remainders under the assumption of Forcing Axioms. In particular, we prove that a strong version of Todorčević's \OCA and Martin's Axiom at level ℵ1 imply: (i) that if X and Y are locally compact second countable topological spaces, then all homeomorphisms between βX∖ X and βY∖ Y are induced by homeomorphisms between cocompact subspaces of X and Y; (ii) that all automorphisms of the corona algebra of a separable C^*-algebra are trivial in a topological sense; (iii) that if A is a unital separable infinite-dimensional C^*-algebra, the corona algebra of A⊗ \mathcal K(H) does not embed into the Calkin algebra. All these results do not hold under the Continuum Hypothesis.