# 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
*