EVENT DETAILS AND ABSTRACT

Title: Twists of stable homotopy theory
Speaker: Tasos Moulinos
Speaker Info: IAS/Paris 13
Brief Description:
Special Note:
Abstract:

Twisted stable homotopy theory was introduced by C. Douglas in his 2005 PhD thesis, to accomodate a need in Floer homotopy theory, of dealing with infinite-dimensional manifolds that are "non-trivially polarised". Roughly one can think of a twisted spectrum over a fixed topological space B as a global section of a bundle of stable infinity-categories over B, which has fiber the category of spectra. I will talk about recent work developing the theory of twisted spectra from an infinity-categorical perspective. I will describe several ways of thinking about such objects, as well how their ensuing functoriality is determined by being fibered over the Brauer space of the sphere spectrum.  I will also mention some examples, both of an elementary nature and some arising from Seiberg-Witten Floer theory. This is joint work with Alice Hedenlund.