Explicit Generators of the Steinberg Module of the Mapping Class Group

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J. Math. Sci. Univ. Tokyo
Vol. 33 (2026), No. 1, Page 1-19.

Irmer, I.
Explicit Generators of the Steinberg Module of the Mapping Class Group
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Abstract:
A conjecture of Broaddus is proven, giving a simple characterisation of a representative of the unique orbit of the action of the mapping class group on the homology of Harvey’s complex of curves for any genus surface. As an application, the kernel of the action of the mapping class group of a genus $g$ surface on the Steinberg module is shown to be trivial.

Keywords: Mapping class groups, Moduli space, Morse Theory.

Mathematics Subject Classification (2020): Primary 57K20. Secondary 57R70.

Received: 2023-12-15

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