Speaker: Alice Hedenlund - Uppsala University
Abstract: Twisted stable homotopy theory was introduced by C. Douglas in his 2005 PhD thesis, meeting a particular need in Floer homotopy theory to deal with infinite-dimensional manifolds that are “non-trivially polarised”. Roughly, one could think of twisted spectra as arising as sections of a bundle of categories whose fibre is the category of spectra. There are multiple ways of rigorously making sense of this: using sheaves of categories, local systems of categories, or modules over Thom spectra. While twisted spectra are essential when constructing stable Floer homotopy types, and may provide a better understanding of the homotopy theoretic underpinning of Floer theory, they are also interesting in their own right from a purely homotopy theoretic point of view, being the obvious generalisation of parametrised spectra (which would correspond to sections of a “trivial bundle”). In this talk I will give an expository talk on twisted parametrised spectra and explain how they naturally appear in Seiberg-Witten Floer theory. This will touch on some of my joint work in progress with S. Behrens, T. Kragh, and T. Moulinos.