# Seminar on the s-cobordism theorem and surgery theory

Prof. Bernd Ammann,

# Seminar delayed to the winter term due to the corona crisis

## Content of the Seminar

The seminar is an advanced reading seminar in which we read a book in preparation by Crowley, Lück and Macko on surgery theory.
In the first talks we will study handlebody decompositions of bordisms and we will define Whitehead groups. This will allow us to formulate and prove the s-cobordism theorem, which is a generalization of the h-cobordism theorem to non-simply-connected manifolds.

This will lead us to Whitehead torsion and Reidemeister torsion which will be studied both from the geometric and algebraic point of view.

The remaining part of the seminar is dominated by the question whether a given CW-comples is homotopy equivalent to a topological manifold, and if it is, whether it is even homotopy equivalent to a smooth manifold.

These questions lead to a long exact sequence, the surgery exact sequence. This sequence exists in several versions, depending on whether we treat smooth, piecewise linear or topological manifolds.

## Literature

We do not take any responsibility for the following external links.
## Requirements

Participants should have some experience with Morse functions and surgery theory. It is helpful if the participants are familiar with the proof of the h-cobordism theorem although the required knowledge can also be obtained by reading Milnor's book listed above as a reference.
## Time and Place

Monday 16.15-18.00 in M103
## Program

The program will be available soon.
The first few talks are already visible here.
## Registration

If you are interested in joining the seminar, please send an email to Bernd Ammann.
## Related web pages

Bernd Ammann, 15.07.2020

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