Mapping class group actions on configuration spaces and the Johnson filtration

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Let Fn(Σg,1) denote the configuration space of n ordered points on the surface Σg,1 and let Γg,1 denote the mapping class group of Σg,1. We prove that the action of Γg,1 on Hi(Fn(Σg,1); ℤ) is trivial when restricted to the ith stage of the Johnson filtration J(i) ⊂ Γg,1. We give examples showing that J(2) acts nontrivially on H3(F3(Σg,1)) for g ≥ 2, and provide two new conceptual reinterpretations of a certain group introduced by Moriyama.

OriginalsprogEngelsk
TidsskriftTransactions of the American Mathematical Society
Vol/bind375
Udgave nummer8
Sider (fra-til)5461-5489
ISSN0002-9947
DOI
StatusUdgivet - 2022

Bibliografisk note

Funding Information:
Received by the editors August 30, 2021, and, in revised form, November 29, 2021. 2020 Mathematics Subject Classification. Primary 55R80, 57K20. 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.

Publisher Copyright:
© 2022 American Mathematical Society.

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