Matthew Stoffregen: A Seiberg–Witten Floer stable homotopy type

Abstract: We give a brief introduction to Floer homology and homotopy, from the Seiberg–Witten point of view. We will then discuss Manolescu's version of finite-dimensional approximation for rational homology spheres. We prove that a version of finite-dimensional approximation for the Seiberg–Witten equations associates equivariant spectra to a large class of three-manifolds. We give some applications to the the study of four-manifolds. This is joint work with Hirofumi Sasahira.