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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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Mapping class group actions on configuration spaces and the Johnson filtration
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by Andrea Bianchi, Jeremy Miller and Jennifer C. H. Wilson PDF
Trans. Amer. Math. Soc. 375 (2022), 5461-5489 Request permission


Let $F_n(\Sigma _{g,1})$ denote the configuration space of $n$ ordered points on the surface $\Sigma _{g,1}$ and let $\Gamma _{g,1}$ denote the mapping class group of $\Sigma _{g,1}$. We prove that the action of $\Gamma _{g,1}$ on $H_i(F_n(\Sigma _{g,1});\mathbb {Z})$ is trivial when restricted to the $i$th stage of the Johnson filtration $\mathcal {J}(i)\subset \Gamma _{g,1}$. We give examples showing that $\mathcal {J}(2)$ acts nontrivially on $H_3(F_3(\Sigma _{g,1}))$ for $g\ge 2$, and provide two new conceptual reinterpretations of a certain group introduced by Moriyama.
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Additional Information
  • Andrea Bianchi
  • Affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, Copenhagen 2100, Denmark
  • MR Author ID: 1324567
  • ORCID: 0000-0003-0209-6416
  • Email:
  • Jeremy Miller
  • Affiliation: Department of Mathematics, Purdue University, 150 North University, West Lafayette, Indiana 47907
  • MR Author ID: 1009804
  • Email:
  • Jennifer C. H. Wilson
  • Affiliation: Department of Mathematics, University of Michigan, 530 Church St., Ann Arbor, Michigan 48109
  • MR Author ID: 906642
  • ORCID: 0000-0002-6601-7468
  • Email:
  • Received by editor(s): August 30, 2021
  • Received by editor(s) in revised form: November 29, 2021
  • Published electronically: May 4, 2022
  • Additional Notes: The first author was supported by the Danish National Research Foundation through the Centre for Geometry and Topology (DNRF151) and the European Research Council under the European Union Horizon 2020 research and innovation programme (grant agreement No. 772960).
    The second author was supported in part by NSF grant DMS-1709726 and a Simons Foundation Collaboration Grants for Mathematicians.
    The third author was supported in part by NSF grant DMS-1906123.
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 5461-5489
  • MSC (2020): Primary 55R80, 57K20
  • DOI:
  • MathSciNet review: 4469226