Chern classes in equivariant bordism

Abstract

We introduce Chern classes in $U(m)$-equivariant homotopical bordism that refine the Conner-Floyd-Chern classes in the $MU$-cohomology of $BU(m)$. 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.

References in corpus (2)

• Splittings of global Mackey functors and regularity of equivariant Euler classes
• The completion and local cohomology theorems for complex cobordism for all compact Lie groups