Disordered arcs and Harer stability

Oscar Harr; Max Vistrup; Nathalie Wahl

doi:10.21136/hs.2024.04

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arXiv · 2211.03858

Disordered arcs and Harer stability

Oscar Harr·Max Vistrup·Nathalie Wahl

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Abstract

We give a new proof of homological stability with the best known isomorphism range for mapping class groups of surfaces with respect to genus. The proof uses the framework of Randal-Williams-Wahl and Krannich applied to disk stabilization in the category of bidecorated surfaces, using the Euler characteristic instead of the genus as a grading. The monoidal category of bidecorated surfaces does not admit a braiding, distinguishing it from previously known settings for homological stability. Nevertheless, we find that it admits a suitable Yang-Baxter element, which we show is sufficient structure for homological stability arguments.

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Oscar Harr, Max Vistrup, Nathalie Wahl. 2022-11-07. Disordered arcs and Harer stability. https://doi.org/10.21136/hs.2024.04

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