Abstract
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.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Transactions of the American Mathematical Society |
| Vol/bind | 375 |
| Udgave nummer | 8 |
| Sider (fra-til) | 5461-5489 |
| ISSN | 0002-9947 |
| DOI | |
| Status | Udgivet - 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.
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