• 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

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>>> 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.

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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.

Talks

Date	Title	Speaker
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
2021
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
23.02.

Literature:

• 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.