I will explain a direct way for defining the Floer homotopy groups of a (framed) manifold flow category in the sense of Cohen Jones and Segal, which does not require any sophisticated tools from homotopy theory (in particular, the notion of a spectrum is not required for the definition). The key point is to work on the geometric topology side of the Pontryagin-Thom construction.

Time permitting, I will also discuss various generalizations which are relevant to Floer theory, and well as joint work in progress with Blumberg for building a spectrum from the new point of view (should you feel that this is needed).