Equivariant bordism and Thom spectra

Speaker: Emma Brink ，Universität Bonn       

Inviter: 邹佛灵

Title: Equivariant bordism and Thom spectra

Language: English

Time & Venue: 2026.04.27  16:00-17:00   Zoom: 6817169181 Password: 211748

Abstract: In this talk, we explore the relation between bordism theories and Thom spectra in equivariant homotopy theory.For a compact Lie group G, we describe a version of G-equivariant geometric bordism with respect to a given stable tangential structure, and we define an equivariant Thom spectrum functor using parametrized homotopy theory.Equivariant bordism admits a Thom-Pontryagin comparison map to the homology theory represented by the associated Thom spectrum. The main result is that the Thom-Pontryagin map is an isomorphism when the connected component of G is central - for example if G is a product of a finite group and a torus. And when G is not of this type, geometric bordism is not represented by a genuine G-spectrum as it fails to admit certain Wirthmüller isomorphisms. This extends work of tom Dieck and Schwede for unoriented bordism to very general tangential structures.