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

• Diarmuid Crowley, Wolfgang Lück, Tibor Macko, a book project with the title: Surgery Theory: Foundations
• Wikipedia page on the Surgery exact sequence
• John Milnor: Lectures on the h-cobordism theorem

• To register, please send an email to Bernd Ammann
• Registration for course work/examination/ECTS: FlexNow

• Presentation: Giving a seminar talk of roughly 90 minutes

• Detailed written report of the seminar talk

• Benotet:
  • O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus dem Seminarvortrag
• Unbenotet:
  • O. g. Studienleistung