Invariant chains and the homology of quotient spaces

dc.creatorKnudson, Kevin P.
dc.date2004-09-08
dc.date.accessioned2026-07-07T05:11:56Z
dc.date.available2026-07-07T05:11:56Z
dc.descriptionFor 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.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0409133
dc.identifierhttp://arxiv.org/abs/math/0409133
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72412
dc.subjectAlgebraic Topology
dc.titleInvariant chains and the homology of quotient spaces
dc.typetext

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