On a spectral sequence for twisted cohomologies

2009/11/07 by Weiping Li, Li, Weiping, Xiugui Liu +3
Mathematics · #57Q10 (Secondary) #58J40 #58J52 (Primary) #81T30 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:57Q10 #msc:58J40 #msc:58J52 #msc:81T30

paper · pdf · doi:10.48550/arxiv.0911.1417

25 pages

arxiv created 2010/05/04 · arxiv updated 2010/05/06

Abstract

Let (Ω^∗(M), d) be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there are a twisted de Rham cochain complex (Ω^∗(M), d+H_\wedge) and its associated twisted de Rham cohomology H^*(M,H). We show that there exists a spectral sequence \E^{p, q}_r, d_r\ derived from the filtration F_p(Ω^∗(M))=\bigoplus_{i≥ p}Ωⁱ(M) of Ω^∗(M), which converges to the twisted de Rham cohomology H^*(M,H). We also show that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.

Related

• Blow-up formulae for twisted cohomologies with supports
• Twisted K-theory and cohomology
• On the blow-up formula of twisted de Rham cohomology
• A vanishing theorem in twisted de Rham cohomology
• Twisted entire cyclic cohomology, J-L-O cocycles and equivariant spectral triples