A Spectral sequence for polynomially bounded cohomology

Abstract

We construct an analogue of the Lyndon-Hochschild-Serre spectral sequence in the context of polynomial cohomology, for group extensions. If G is an extension of Q by H, then the spectral sequence converges to the polynomial cohomology of G. For the polynomial extensions of Noskov with normal subgroup isocohomological, the E_2 term is the polynomial cohomology of Q with coefficients in the polynomial cohomology of H. When both Q and H are isocohomological G must be as well. By referencing results of Connes-Moscovici and Noskov, if Q and H are both isocohomological and have the Rapid Decay property of Jolissaint, then G satisfies the Novikov Conjecture.

20 pages, no figures

References in corpus (4)

• Embeddings of derived categories of bornological modules
• Combable groups have group cohomology of polynomial growth
• Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture
• The isocohomological property, higher Dehn functions, and relatively hyperbolic groups

Cited by in corpus (1)

• B-Bounded cohomology and applications