Home Article Information
Bulletin of the Iranian Mathematical Society
Journal Archive
Volume Volume 43 (2017)
Volume Volume 42 (2016)
Volume Volume 41 (2015)
Volume Volume 40 (2014)
Volume Volume 39 (2013)
Volume Volume 38 (2012)
Volume Volume 37 (2011)
Volume Volume 36 (2010)
Volume Volume 35 (2009)
Volume Volume 34 (2008)
Volume Volume 33 (2007)
Volume Volume 32 (2006)
Volume Volume 31 (2005)
Volume Volume 30 (2004)
Volume Volume 29 (2003)
Volume Volume 28 (2002)
Volume Volume 27 (2001)

Ring structures of mod p equivariant cohomology rings and ring homomorphisms between them

Article 30, Volume 38, Issue 2, July 2012, Page 529-542  XML PDF (229 K)
Document Type: Research Paper
Authors
Yanchang Chen1; Yanying Wang 2
1College of Mathematics and Information Science, Hebei Normal University, Yuhua Road 113, Shijiazhuang 050016, P. R. China
2College of Mathematics and Information Science, Hebei Normal University, Yuhua Road 113, Shijiazhuang 050016, P. R. China
Abstract
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes it possible to determine the number of equivariant cohomology rings (up to isomorphism) of such 2-dimensional G-manifolds. Moreover, we obtain a description of the ring homomorphism between equivariant cohomology rings of such two G-manifolds induced by a G-equivariant map, and show a characterization of the ring homomorphism.
Keywords
G-manifold; equivariant index; equivariant cohomology; ring homomorphism
Main Subjects
55-XX Algebraic topology; 57-XX Manifolds and cell complexes; 58-XX Global analysis, analysis on manifolds
Statistics
Article View: 1,469
PDF Download: 1,222