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Fakultät für Mathematik Universität Regensburg
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s-cobordism theorem and surgery theory
Semester
SoSe 2020

Lecturer
Bernd Ammann

Type of course (Veranstaltungsart)
Seminar

Contents
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 external links.

Recommended previous knowledge
For participation one 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/Date
Monday 16-18

Location
M103

Course homepage
http://www.mathematik.uni-regensburg.de/ammann/lehre/2020s_s-cobordism/
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • To register, please send an email to Bernd Ammann
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Presentation: Giving a seminar talk of roughly 90 minutes
Examination (Prüfungsleistungen)
  • Detailed written report of the seminar talk
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus dem Seminarvortrag
  • Unbenotet:
    • O. g. Studienleistung
Modules
MV, MSem

ECTS
Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn
vor WS 15/16
Druckansicht