Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Inner products and ℤ/p

Inner products and ℤ/p Forum Math. 15 (2003), 439­454 ( de Gruyter 2003 ´ Inner products and Z/p-actions on Poincare duality spaces Bernhard Hanke (Communicated by Frederick Cohen) ´ Abstract. Let Z=p act on an Fp -Poincare duality space X, where p is an odd prime number. We derive a formula that expresses the Fp -Witt class of the fixed point set X Z=p in terms of the Fp ½Z=p-algebra H Ã ðX ; Fp Þ, if H Ã ðX ; Zð pÞ Þ does not contain Z=p as a direct summand. This extends previous work of Alexander and Hamrick, where the orientation class of X is supposed to be liftable to an integral class. 2000 Mathematics Subject Classification: 18G40, 57S17; 57P10. ´ Given a prime p and a finite dimensional Z=p-CW complex X which fulfills Poincare duality over Fp , a theorem of Bredon ([4]) and Chang and Skjelbred ([7]) predicts the ´ fixed point set components of this Z=p-action to be Fp -Poincare duality complexes, as well. Furthermore, the formal dimension (with Fp -coecients) of each fixed point component has the same parity as the formal dimension of X. It is the purpose of this paper to derive an analogue http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Inner products and ℤ/p

Hanke, Bernhard
Forum Mathematicum , Volume 15 (3) – May 20, 2003
Download PDF
16 pages

Loading next page...
 
/lp/de-gruyter/inner-products-and-p-UcLfyBizWG

References (21)

Publisher
de Gruyter
Copyright
Copyright © 2003 by Walter de Gruyter GmbH & Co. KG
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.2003.023
Publisher site
See Article on Publisher Site

Abstract

Forum Math. 15 (2003), 439­454 ( de Gruyter 2003 ´ Inner products and Z/p-actions on Poincare duality spaces Bernhard Hanke (Communicated by Frederick Cohen) ´ Abstract. Let Z=p act on an Fp -Poincare duality space X, where p is an odd prime number. We derive a formula that expresses the Fp -Witt class of the fixed point set X Z=p in terms of the Fp ½Z=p-algebra H Ã ðX ; Fp Þ, if H Ã ðX ; Zð pÞ Þ does not contain Z=p as a direct summand. This extends previous work of Alexander and Hamrick, where the orientation class of X is supposed to be liftable to an integral class. 2000 Mathematics Subject Classification: 18G40, 57S17; 57P10. ´ Given a prime p and a finite dimensional Z=p-CW complex X which fulfills Poincare duality over Fp , a theorem of Bredon ([4]) and Chang and Skjelbred ([7]) predicts the ´ fixed point set components of this Z=p-action to be Fp -Poincare duality complexes, as well. Furthermore, the formal dimension (with Fp -coecients) of each fixed point component has the same parity as the formal dimension of X. It is the purpose of this paper to derive an analogue

Journal

Forum Mathematicum – de Gruyter

Published: May 20, 2003

There are no references for this article.