Equivariant bordism of surfaces and counterexamples to the evenness conjecture

Equivariant bordism of surfaces and counterexamples to the evenness conjecture

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Eric Samperton, University of Illinois at Urbana-Champaign

Online Talk 

Zoom link: https://princeton.zoom.us/j/96282936122

Passcode: 998749

Let G be a finite group.  The G-equivariant bordism ring is a module over the usual (non-equivariant) bordism ring. It was observed in various works in the 1970s that for G abelian or metacyclic, the G-equivariant unitary bordism ring is a free module with generators in even degrees. Later Comezaña conjectured this should be true for general G, and then Uribe promoted the problem at ICM 2018, where he called it the “evenness conjecture for equivariant bordism.”  We will show the conjecture is false by finding explicit counterexamples.  We then build on these techniques to explicitly compute the 2-dimensional G-equivariant unitary and oriented bordism groups for all finite groups G.

This talk is based on joint work with Andrés Ángel, Carlos Segovia and Bernardo Uribe.