A degree formula for equivariant cohomology
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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.References
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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
- Received by editor(s): January 31, 2011
- Received by editor(s) in revised form: February 1, 2012
- Published electronically: September 19, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 309-339
- MSC (2010): Primary 55N91; Secondary 13H15, 13D40
- DOI: https://doi.org/10.1090/S0002-9947-2013-05828-X
- MathSciNet review: 3118398