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arXiv · 2601.22303

The Homology of Complex Equivariant Bordism

Julius Groenjes
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Abstract

Let $A$ be an abelian compact Lie group and let $E$ be an oriented $A$-spectrum. We compute the $E$-homology of tom Dieck's homotopical $A$-equivariant complex bordism spectrum $MU_A$ in two ways, correcting an error in Cole-Greenlees-Kriz (2002). Additionally, we calculate the $E$-homology of the geometric $A$-equivariant complex bordism spectrum $mU_A$.

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Julius Groenjes. 2026-01-29. The Homology of Complex Equivariant Bordism. https://arxiv.org/abs/2601.22303

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