Mathematics Topology Seminar - Manuel Krannich

Warning Icon This event is in the past.

Date: March 19, 2020
Time: 2:00 p.m. - 3:00 p.m.
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
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.


Department of Mathematics



Add to my calendar

Save to iCal