Advanced Topics in Topology:
Equivariant stable homotopy theory (V5D1)
Winter term 2019/20

Lecture course, Tuesday 10:15 -- 12:00 and Thursday 14:15-16:00, SR 0.011 (Mathematikzentrum)

Stefan Schwede
Endenicher Allee 60, room 4.008
Email : schwede (at) math.uni-bonn.de

Topics

The class is an introduction to equivariant stable homotopy theory for finite groups of equivariance; we will use orthogonal G-spectra as our model. Some topics to be covered include: equivariant stable homotopy groups, the `genuine' G-equivariant stable homotopy category, the Wirthmüller isomorphism, transfers, genuine and geometric fixed points, and the tom Dieck splitting. Along the way, we'll discuss many examples.

References:
- A. Blumberg, The Burnside category. Lecture notes for M392C (Topics in Algebraic Topology), Spring 2017, U Texas, Austin.
- M. Mandell, J. P. May, Equivariant orthogonal spectra and S-modules. Mem. Amer. Math. Soc. 159 (2002), no. 755, x+108 pp.
- S. Schwede, Lecture notes on equivariant stable homotopy theory.
- Chapter 3 of S. Schwede, Global homotopy theory, New Mathematical Monographs 34. Cambridge University Press, Cambridge, 2018. xviii+828 pp. [download]

Survey articles:
- J. F. Adams, Prerequisites (on equivariant stable homotopy) for Carlsson's lecture. Algebraic topology, Aarhus 1982, 483-532. Lecture Notes in Math. 1051, Springer-Verlag, 1984.
- J. P. C. Greenlees, J. P. May, Equivariant stable homotopy theory. Handbook of algebraic topology, 277-323. North-Holland, Amsterdam, 1995.

Prerequisites

Prerequisites for this class are the contents of the classes Topology 1-2 and Algebraic Topology 1-2. There will not be any exercise sessions for this class.

Exam

The oral exams will take place on Thursday, January 30, 2020. The second exam will take place on Wednesday, March 25, 2020.


S. Schwede, 28.10.2019