Spectral sequences, Massey products and homology of covering spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915619235954688 |
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| author | Liu, Yongqiang Maxim, Laurentiu Wang, Botong |
| author_facet | Liu, Yongqiang Maxim, Laurentiu Wang, Botong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral sequences, Massey products and homology of covering spaces Liu, Yongqiang Maxim, Laurentiu Wang, Botong Algebraic Topology 55N25, 55T99, 57M05 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. |
| title | Spectral sequences, Massey products and homology of covering spaces |
| topic | Algebraic Topology 55N25, 55T99, 57M05 |
| url | https://arxiv.org/abs/2511.11893 |