Invariant chains and the homology of quotient spaces
| dc.creator | Knudson, Kevin P. | |
| dc.date | 2004-09-08 | |
| dc.date.accessioned | 2026-07-07T05:11:56Z | |
| dc.date.available | 2026-07-07T05:11:56Z | |
| dc.description | For a finite group G and a finite G-CW-complex X, we construct groups H_\bullet(G,X) as the homology groups of the G-invariants of the cellular chain complex C_\bullet(X). These groups are related to the homology of the quotient space X/G via a norm map, and therefore provide a mechanism for calculating H_\bullet(X/G). We compute several examples and provide a new proof of ``Smith theory": if G=Z/p and X is a mod p homology sphere on which G acts, then the subcomplex X^G is empty or a mod $p$ homology sphere. We also get a new proof of the Conner conjecture: If G=Z/p acts on a Z-acyclic space X, then X/G is Z-acyclic. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409133 | |
| dc.identifier | http://arxiv.org/abs/math/0409133 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72412 | |
| dc.subject | Algebraic Topology | |
| dc.title | Invariant chains and the homology of quotient spaces | |
| dc.type | text |