# GT Seminar with Thomas Kragh (Uppsala university)

- Date: 8 December 2022, 13:15–14:15
- Location: Ångström Laboratory, room Å64119 and on zoom https://uu-se.zoom.us/j/68210068219
- Type: Seminar
- Lecturer: Thomas Kragh (Uppsala university)
- Organiser: Matematiska institutionen
- Contact person: Noémie Legout

Welcome to this seminar hold by Thomas Kragh (Uppsala university) with title "Seiberg-Witten Floer Homotopy Types II: Family Floer theory and twisted spectra".

**Abstract:** I will start by discussing the example that was discussed at length last time during Alice's talk, and provide some variations and context (relating it to some notions of family Floer theory in cotangent bundles, background classes, partially wrapping, and micro-local support - hoping that each audience member will find at least one of these relations provides some insight into such examples and why they are interesting). I will then describe how to construct somewhat explicit twisted spectra out of finite dimensional approximations and Conley indices in the Seiberg-Witten (SWF) setting (this setting is actually much easier than the cotangent bundle). I will then talk about other twisted categories than that of twisted spectra. In particular I will describe how S^1-equivariant homotopy theory naturally arises in this context and how we actually construct a "twisted parametrized S1-equivariant spectrum" representing SWF (I will not assume much knowledge about any of these stable categories - and I will try and keep most of the general discussion at a heuristic level). This is joint work with A. Hedenlund and S. Behrens.

See upcoming seminars in our seminar series on Geometry and Topology (GT).