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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A degree formula for equivariant cohomology


Author: Rebecca Lynn
Journal: Trans. Amer. Math. Soc. 366 (2014), 309-339
MSC (2010): Primary 55N91; Secondary 13H15, 13D40
Published electronically: September 19, 2013
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Abstract: The primary theorem of this paper concerns the Poincaré (Hilbert) series for the cohomology ring of a finite group $ G$ with coefficients in a prime field of characteristic $ p$. This theorem is proved using the ideas of equivariant cohomology whereby one considers more generally the cohomology ring of the Borel construction $ H^*(EG \times _G X)$, where $ X$ is a manifold on which $ G$ acts. This work results in a formula that computes the ``degree'' of the Poincaré series in terms of corresponding degrees of certain subgroups of the group $ G$. In this paper, we discuss the theorem and the method of proof.


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Additional Information

Rebecca Lynn
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80538
Address at time of publication: Department of Mathematics, Friends University, Wichita, Kansas 67213
Email: lynn@math.colostate.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05828-X
PII: S 0002-9947(2013)05828-X
Received by editor(s): January 31, 2011
Received by editor(s) in revised form: February 1, 2012
Published electronically: September 19, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.