19223811 Forschungsmodul: Topologie “Equivariant stable homotopy theory”
- FU-Students should register via Campus Management.
- Non-FU-students should register via MyCampus/Whiteboard.
- The course will be held remotely using WebEx.
Winter Term 2020/2021
Dozenten: Dr. Gabriel Angelini-Knoll, Prof. Dr. Elmar Vogt
>>> Please note that the start of the Winter Term has been postponed two weeks. <<<
Time and place: Tuesday, 4pm -- 6pm, online
Leistungsnachweis/criteria for proof of performance:
Grade and credit points will be awarded based on a presentation and written summary.
Prerequisites: We assume basic knowledge of topology as taught in Topology I and II.
Content: The seminar will cover advanced topics from topology and homotopy theory.
The study of group actions is ubiquitous in mathematics as historically groups arose from the study of symmetries. The study of continuous group actions on topological spaces is therefore fundamental to many areas of mathematics. Stable equivariant homotopy theory provides a world for studying duality in the setting of spaces with a continuous action of a group, such as Spanier-Whitehead duality. Equivariant stable homotopy theory has a long rich history and it remains an active area of research. In part, this is because it has lead to resolutions of open problems in other areas of topology, which on the face of them, do not seem related to equivariant stable homotopy theory at all.
This seminar will begin with some non-equivariant stable homotopy theory and equivariant unstable homotopy theory. We will then learn the fundamental constructions in equivariant stable homotopy theory and carefully prove some of the fundamental results in the subject.
|03.11.||Talk 1: Organization and overview||Gabriel Angelini-Knoll|
|10.11.||Talk 2: Unstable equivariant homotopy||Elmar Vogt|
|17.11.||Talk 3: The Spanier Whitehead category and duality||Gabriel Angelini-Knoll|
|24.11.||Talk 4: Orthogonal spectra||William Bitsch|
|01.12.||Talk 5: Equivariant Orthogonal spectra||Tianzhi Yang|
|08.12.||Talk 6: Examples of equivariant orthogonal spectra||Fabian Gringel|
|15.12.||Talk 7: Equivariant homotopy groups||Roger Bergada|
|05.01.||Talk 8: Loop and suspension by representations||Jessica Gonzalez|
|12.01.||Talk 9: Mapping cone and homotopy fibers||Vittorio Di Fraia|
|19.01.||Talk 10: Set up for the Wirthm¨uller isomorphism||Evgeniya Lagoda|
|26.01.||Talk 11: The Wirthm¨uller isomorphism||Ferry Saavedra|
|02.02.||Talk 12: Transfers||Gabriel Angelini-Knoll|
|09.02.||Talk 13: Mackey functors||Elmar Vogt|
|16.02.||Talk 14: The Tom Dieck splitting||Georg Lehner|
- J.F. Adams: Prerequisites (on equivariant stable homotopy) for Carlsson's lecture. In Algebraic topology, Aarhus 1982 (Aarhus, 1982), volume 1051 of Lecture Notes in Math., pages 483–532. Springer, Berlin, 1984.
- Stefan Schwede: Lectures on equivariant stable homotopy theory, 2020.