Towards a nonabelian cohomology of forms

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dc.creatorPatel, Mukul
dc.date2004-12-23
dc.date2005-03-07
dc.date.accessioned2026-07-07T05:15:38Z
dc.date.available2026-07-07T05:15:38Z
dc.descriptionWe consider a simple and natural coboundary operator, on the Lie algebra valued differential forms on a manifold, which in the abelian case reduces to usual exterior derivative of such forms. Using the corresponding de Rham cohomology Lie superalgebra H*(M,G) we obtain numerical smooth invariants--as opposed to homotopy invariants--for manifolds. The corresponding Hodge theory yields finiteness of nonabelian Betti numbers. A genralized Poincaré lemma, along with a Poincaré duality, a Mayer-Vietoris, and a particularly empowered Bockstein makes our cohomology computable. Bockstein also allows us to relate (nonabelian) diffeomorphism invariants to (abelian) homotopy invariants.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0412481
dc.identifierhttp://arxiv.org/abs/math/0412481
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73693
dc.subjectGeometric Topology
dc.subjectAlgebraic Topology
dc.subject57Rxx;55Nxx
dc.titleTowards a nonabelian cohomology of forms
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