Cut-and-paste K-theory of manifolds and SK-automorphisms

This is an online seminar. It is part of an approximately monthly series associated with the PIMS CRG in Diagram Categories in Homotopy Theory.

The Zoom information is https://ubc.zoom.us/j/67108700370?pwd=a3trUMqdCrEbOGbr3dGkYfEvTU8eIp.1

Meeting ID: 671 0870 0370
Passcode: 805484
 

Given two manifolds M and N, one can ask whether it is possible to cut M up into pieces and reassemble them to obtain N. This “cut-and-paste” (SK) relation fits into the framework of scissors congruence K-theory, which is an extension of higher algebraic K-theory to more general settings. In this talk, we will discuss a new model for the cut-and-paste K-theory of manifolds, modeled on Waldhausen’s S-dot construction, and describe how the first K-group is related to SK-automorphisms of manifolds, i.e. the ways a manifold can be SK-equivalent to itself. This talk is based on joint work with Maru Sarazola.