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arXiv · 2303.12366

Chern classes in equivariant bordism

Stefan Schwede
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Abstract

We introduce Chern classes in $U(m)$-equivariant homotopical bordism that refine the Conner-Floyd-Chern classes in the $MU$-cohomology of $B U(m)$. For products of unitary groups, our Chern classes form regular sequences that generate the augmentation ideal of the equivariant bordism rings. Consequently, the Greenlees-May local homology spectral sequence collapses for products of unitary groups. We use the Chern classes to reprove the $MU$-completion theorem of Greenlees-May and La Vecchia.

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Stefan Schwede. 2023-03-22. Chern classes in equivariant bordism. https://doi.org/10.1017/fms.2023.124

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