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arXiv · 2511.11893

Spectral sequences, Massey products and homology of covering spaces

Yongqiang Liu·Laurentiu Maxim·Botong Wang
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Abstract

We revisit the equivariant spectral sequence considered by Papadima-Suciu, and show that all its differentials are computed by higher order Massey products. As a first application, we extend to arbitrary field coefficients results of Pajitnov relating the size of Jordan blocks for the eigenvalue 1 part of the Alexander modules to the length of nonvanishing Massey products in cohomology. We also give computable upper bounds for the mod p Betti numbers of prime power cyclic covers, and resp. for the ranks of the cohomology groups with coefficients in a prime order rank one local system. Under suitable conditions, these bounds are improvements of the ones obtained by Papadima-Suciu. We also specialize these results to the case of hyperplane arrangement complements, showing, e.g., that vanishing of higher-order Massey products implies that the mod p Betti numbers of prime p tower cyclic covers are combinatorially determined.

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Yongqiang Liu, Laurentiu Maxim, Botong Wang. 2025-11-14. Spectral sequences, Massey products and homology of covering spaces. https://arxiv.org/abs/2511.11893

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