Poincaré duality in P.A. Smith theory
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- by Christopher Allday, Bernhard Hanke and Volker Puppe PDF
- Proc. Amer. Math. Soc. 131 (2003), 3275-3283 Request permission
Abstract:
Let $G=S^1$, $G=\mathbb {Z}/p$ or more generally $G$ be a finite $p$-group, where $p$ is an odd prime. If $G$ acts on a space whose cohomology ring fulfills Poincaré duality (with appropriate coefficients $k$), we prove a mod $4$ congruence between the total Betti number of $X^G$ and a number which depends only on the $k[G]$-module structure of $H^*(X;k)$. This improves the well known mod $2$ congruences that hold for actions on general spaces.References
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Additional Information
- Christopher Allday
- Affiliation: Department of Mathematics, University of Hawaii, 2565 Mc Carthy Mall, Honolulu, Hawaii 96822
- Email: chris@math.hawaii.edu
- Bernhard Hanke
- Affiliation: Department of Mathematics, Universität München, Theresienstr. 39, 80333 München, Germany
- Email: hanke@rz.mathematik.uni-muenchen.de
- Volker Puppe
- Affiliation: Department of Mathematics, Universität Konstanz, 78457 Konstanz, Germany
- Email: Volker.Puppe@uni-konstanz.de
- Received by editor(s): September 20, 2001
- Received by editor(s) in revised form: May 3, 2002
- Published electronically: February 6, 2003
- Additional Notes: The second author holds a DFG research grant. He thanks the University of Notre Dame for its hospitality during the work on this paper
- Communicated by: Paul Goerss
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3275-3283
- MSC (2000): Primary 57S10, 57P10, 55N10; Secondary 55N91
- DOI: https://doi.org/10.1090/S0002-9939-03-06856-4
- MathSciNet review: 1992869