Introduction
This course reviewed the foundations for equivariant stable homotopy theory in the context of orthogonal G-spectra. The standard reference for this theory is the work [2] by Mandell and May. Its relevance has recently been highlighted by its application in the solution of the Kervaire invariant one problem announced by Hill, Hopkins and Ravenel in 2008 and developed in the prepublication [1]. The appendices of this preprint contain further material, in particular on the norm construction.
However, the presentation of the material offered by Professor Schwede in this course was in many aspects original and different from these two main sources. For the sake of brevity, the model theory aspects of the theory were skipped. The course concentrated on the case of finite groups (as opposed to compact Lie groups).
First, the (non-equivariant) theory of orthogonal spectra was presented. Then, equivariant orthogonal spectra were constructed, and their corresponding equivariant homotopy groups were defined. Further constructions with equivariant spectra were obtained and the properties of homotopy groups were also considered. One of the main aims of the course came next: the diverse relevant fixed points constructions (naive, homotopy and geometric) and how they relate to each other. This allowed a discussion of the power and norm constructions at the end of the course.
Organizing Committee
| Grup de topologia algebraica de Barcelona (GTAB) |
SPEAKERS
Stefan Schwede, Universität Bonn
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