Differential Geometry Seminar: A connected sum formula for the families Bauer-Furuta invariant

Speaker: Joshua Tomlin (University of Adelaide)

Title: A connected sum formula for the families Bauer-Furuta invariant

Abstract: Seiberg-Witten theory is a branch of 4-manifold topology that has brought with it many striking results since the early 90s. The Bauer-Furuta invariant is a refinement of the integer valued Seiberg-Witten invariant, derived from the stable cohomotopy class of a finite dimensional approximation of the Seiberg-Witten monopole map. By analysing the monopole map rather than its solutions, techniques from algebraic topology can be used to circumvent laborious analytical arguments. In this talk we will define the Bauer-Furuta invariant and sketch a proof of a formula for the Bauer-Furuta invariant of a connected sum. We will touch on how this formula extends to families of four manifolds and how it can be used to obtain a connected sum formula for the families Seiberg-Witten invariant.