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

Lecture course, Tuesays 10:15 -- 12:00 and Thursday 10:15-12:00, 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

There will be oral exams.


S. Schwede, 25.06.2019