Seminar/Lesekurs zur Algebraischen Topologie im Wintersemester 2024/25

Dozent: Prof. Dr. S. Goette

Assistent: Dr. Misha Tëmkin

Was, wann, wo

Seminar/Lesekurs: Di 14-16, SR 125, Ernst-Zermelo-Str. 1

Vorbesprechung: Di 16.07, 16:00 Uhr, SR 125, Ernst-Zermelo-Str. 1

Language: depending on the audience, this course might take place in English or German

Topic:
The paper "The homotopy type of the cobordism category" [1] is about a categorical version of the Pontryagin-Thom isomorphism. With the techniques introduced there, it is possible to prove the Mumford conjecture on the rational cohomology ring of the stable moduli space of Riemann surfaces.
In the reading course, we want to understand the central result: there is a weak homotopy equivalence
α:BCd→Ω∞-1MTO(d).
On the way, we will learn some useful concepts like simplicial sets and their geometric realisations, classifying spaces for bundles of manifolds, and Madsen-Tillmann spectra.
If there is time at the end, we can have a glance at possible applications.

Programme: Here is the preliminary programme.

Literature: (not a complete list)

  1. S. Galatius, I. Madsen, U. Tillmann, M. Weiss, The homotopy type of the cobordism category, Acta Math. 202, No. 2, 195-239 (2009), DOI, arXiv:math/0605249
  2. I. Madsen, M. Weiss, The stable moduli space of Riemann surfaces: Mumford’s conjecture, Ann. of Math., 165 (2007), 843-941. DOI, arXiv:math/0212321
  3. D. Freed, Bordism: Old and New, lecture notes, 2012

Studien- und Prüfungsleistungen

Die verbindlichen Anforderungen für die Studien- und/oder Prüfungsleistung finden Sie im Modulhandbuch, und später zur Info auch hier (ohne Gewáhr).