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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The spectral sequence of an equivariant chain complex and homology with local coefficients
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by Stefan Papadima and Alexander I. Suciu PDF
Trans. Amer. Math. Soc. 362 (2010), 2685-2721 Request permission


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 $H_*(X,\Bbbk )$ and the $\Bbbk \pi _1(X)$-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 $H^*(X,\Bbbk )$, thereby generalizing a result of Cohen and Orlik.
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Additional Information
  • Stefan Papadima
  • Affiliation: Institute of Mathematics Simion Stoilow, P.O. Box 1-764, RO-014700 Bucharest, Romania
  • Email:
  • Alexander I. Suciu
  • Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
  • MR Author ID: 168600
  • ORCID: 0000-0002-5060-7754
  • Email:
  • Received by editor(s): September 29, 2008
  • Published electronically: December 15, 2009
  • Additional Notes: The first author was partially supported by the CEEX Programme of the Romanian Ministry of Education and Research, contract 2-CEx 06-11-20/2006
    The second author was partially supported by NSF grant DMS-0311142
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 2685-2721
  • MSC (2010): Primary 55N25, 55T99; Secondary 20J05, 57M05
  • DOI:
  • MathSciNet review: 2584616