Title: Floer homotopy without spectra
Speaker: Mohammed Abouzaid
Speaker Info: Columbia University
Brief Description: Research Talk
Meeting ID: 922-4351-6463Date: Thursday, May 14, 2020
Meeting Password: first word of the name of the seminar
Abstract: The construction of Cohen-Jones-Segal of Floer homotopy types associated to appropriately oriented flow categories extracts from the morphisms of such a category the data required to assemble an iterated extension of free modules (in an appropriate category of spectra). I will explain a direct (geometric) way for defining the Floer homotopy groups which completely bypasses the algebra. The key point is to work on the geometric topology side of the Pontryagin-Thom construction. Time permitting, I will also explain joint work in progress with Blumberg for building a spectrum from the new point of view, as well as various generalisations which are relevant to Floer theory.