Mathematical Research Letters

Volume 27 (2020)

Number 4

On the $RO(G)$-graded coefficients of dihedral equivariant cohomology

Pages: 1109 – 1128

DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n4.a7

Authors

Igor Kriz (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Yunze Lu (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Abstract

We completely calculate the $RO(G)$-graded coefficients of ordinary equivariant cohomology where $G$ is the dihedral group of order $2p$ for a prime $p \gt 2$ both with constant and Burnside ring coefficients. The authors first proved it for $p = 3$ and then the second author generalized it to arbitrary $p$. These are the first such calculations for a non-abelian group.

Kriz acknowledges the support of a Simons Collaboration Grant.

Received 20 April 2018

Accepted 3 May 2020

Published 14 December 2020