# Mathematics Topology Seminar - Manuel Krannich

This event is in the past.

**Date:**March 19, 2020

**Time:**2:00 p.m. - 3:00 p.m.

**Category:**Seminar

Speaker: **Manuel Krannich, University of Cambridge**

Title: **Pseudoisotopies of even discs and algebraic K-theory of the integers**

Abstract: **There is an intimate connection between algebraic K-theory and the space of pseudo-isotopies P(M) of a compact d-manifold M (that is, diffeomorphisms of a cylinder M x I that are the identity on M x 0 and ∂M x I). Classically, the pseudo-isotopy space P(M) is studied in two steps: there is a stabilisation map P(M)-> P(M x I) which is approximately d/3-connected by a result of Igusa, and the colimit has a description in terms of Waldhausen's algebraic K-theory of spaces due to Waldhausen--Jahren--Rognes' stable parametrised h-cobordism theorem.**

**In this talk, I will focus on the case of an even-dimensional disc and explain a new method to relate its space of pseudo-isotopies to the algebraic K-theory of the integers in a range up to roughly the dimension. This approach is independent of the usual route, does not involve stabilising the dimension, and is homological in nature.**