Mathematics – Algebraic Topology
Scientific paper
2007-08-31
Transactions of the American Mathematical Society 362 (2010), no. 5, 2685-2721
Mathematics
Algebraic Topology
38 pages, 1 figure (section 10 of version 1 has been significantly expanded into a separate paper, available at arXiv:0901.010
Scientific paper
10.1090/S0002-9947-09-05041-7
We study the spectral sequence associated to the filtration by powers of the augmentation ideal on the (twisted) equivariant chain complex of the universal cover of a connected CW-complex X. In the process, we identify the d^1 differential in terms of the coalgebra structure of H_*(X,\k), and the \k\pi_1(X)-module structure on the twisting coefficients. In particular, this recovers in dual form a result of Reznikov, on the mod p cohomology of cyclic p-covers of aspherical complexes. This approach provides information on the homology of all Galois covers of X. It also yields computable upper bounds on the ranks of the cohomology groups of X, with coefficients in a prime-power order, rank one local system. When X admits a minimal cell decomposition, we relate the linearization of the equivariant cochain complex of the universal abelian cover to the Aomoto complex, arising from the cup-product structure of H^*(X,\k), thereby generalizing a result of Cohen and Orlik.
Papadima Stefan
Suciu Alexander I.
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