On Completion and the Evenness Conjecture for Homotopical Equivariant Cobordism

Abstract

We give counterexamples to the evenness conjecture for homotopical equivariant cobordism. To this end, we prove a completion theorem for certain complex cobordism modules which does not involve higher derived functors. A key step in the proof is provided by a certain new relation between Mackey and Borel cohomology.

Keywords

Complex cobordism / Equivariant cobordism / Equivariant spectra / Completion theorem / Evenness conjecture

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Funding

Division of Mathematical Sciences(2023350430)

RIGHTS & PERMISSIONS

Peking University