An equivariant Quillen theorem

Hanke, Bernhard; Wiemeler, Michael

doi:10.1016/j.aim.2018.10.009

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An equivariant Quillen theorem

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Hanke, Bernhard
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.aim.2018.10.009
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arXiv:1711.02399.pdf
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Hanke, B., & Wiemeler, M. (2018). An equivariant Quillen theorem. Advances in Mathematics, 340, 48-75. doi:10.1016/j.aim.2018.10.009.

Cite as: https://hdl.handle.net/21.11116/0000-0003-AD70-C

Abstract

A classical theorem due to Quillen (1969) identifies the unitary bordism ring with the Lazard ring, which represents the universal one-dimensional commutative formal group law. We prove an equivariant generalization of this result by identifying the homotopy theoretic $\mathbb{Z}/2$-equivariant unitary bordism ring, introduced by tom Dieck (1970), with the $\mathbb{Z}/2$-equivariant Lazard ring, introduced by Cole-Greenlees-Kriz (2000). Our proof combines a computation of the homotopy theoretic $\mathbb{Z}/2$-equivariant unitary bordism ring due to Strickland (2001) with a
detailed investigation of the $\mathbb{Z}/2$-equivariant Lazard ring.