Noncommutative Geometry Seminar

Date: October 5, 2022

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Ryo Toyota, TAMU

Title: Controlled K-theory and K-homology

Abstract: I will introduce a new perspective of K-homology of spaces. This work is motivated by a paper of Guoliang Yu, where he showed that the K-theory of the localization algebra is isomorphic to K-homology for finite simplicial complexes. The localization algebra consists of functions from [1,\infty) to Roe algebra whose propagations go to 0. "The reason" we get K-homology is that by focusing operators whose propagation is small, we can recover some local information on spaces we lost by taking Roe algebras. Here we discuss how we can recover K-homology by focusing on operators whose propagation is smaller than a certain threshold r instead of thinking of operator valued functions. I will report what we can prove and what should be true.