Equivariant cohomology and analytic descriptions of ring isomorphisms
| dc.creator | Chen, Bo | |
| dc.creator | Lü, Zhi | |
| dc.date | 2007-03-05 | |
| dc.date | 2008-03-24 | |
| dc.date.accessioned | 2026-07-07T12:42:22Z | |
| dc.date.available | 2026-07-07T12:42:22Z | |
| dc.description | In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a $G$-manifold in terms of algebra, so that we can obtain analytic descriptions of ring isomorphisms among equivariant cohomology rings of such $G$-manifolds, and a necessary and sufficient condition that the equivariant cohomology rings of such two $G$-manifolds are isomorphic. This also leads us to analyze how many there are equivariant cohomology rings up to isomorphism for such $G$-manifolds in 2- and 3-dimensional cases. | |
| dc.description | 20 pages, updated version with two references added | |
| dc.identifier | https://arxiv.org/abs/math/0703083 | |
| dc.identifier | http://arxiv.org/abs/math/0703083 | |
| dc.identifier | Math. Z. 261 (2009), 891-908. | |
| dc.identifier | doi:10.1007/s00209-008-0357-y | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220051 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57S17; 55N91; 58J20 | |
| dc.title | Equivariant cohomology and analytic descriptions of ring isomorphisms | |
| dc.type | text |