Alice Hedenlund: Twisted Spectra

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.

The aim of this talk is to give an introduction to twisted spectra and discuss some of their basic properties, based on joint work in progress with T. Moulinos. I will also outline how they appear naturally in the setting of Floer homotopy theory.