An equivariant Quillen theorem

Bernhard Hanke; Michael Wiemeler

doi:10.1016/j.aim.2018.10.009

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arXiv · 1711.02399

An equivariant Quillen theorem

Bernhard Hanke·Michael Wiemeler

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Abstract

A classical theorem due to Quillen (1969) identifies the unitary bordism ring with the Lazard ring, which classifies 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.

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BibTeX RIS

Bernhard Hanke, Michael Wiemeler. 2017-11-07. An equivariant Quillen theorem. https://doi.org/10.1016/j.aim.2018.10.009

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