Yang-Baxter Elements and a New Proof of Homological Stability for the Mapping Class Group of Surfaces

Explore a 50-minute conference talk by Nathalie Wahl from the University of Copenhagen, presented at the Fields Institute. Delve into the concept of Yang-Baxter elements in monoidal categories and their role in providing a weak form of braiding. Discover how these elements are used to define a semi-simplicial set, which in turn governs homological stability for certain automorphism groups. Learn about the application of this approach to the category of bimarked surfaces, resulting in a direct proof of slope 2/3 stability for the homology of mapping class groups of surfaces. Gain insights into this collaborative research with Oscar Harr and Max Vistrup, presented as part of the Conference on Homotopy Theory with Applications to Arithmetic and Geometry held from June 27-30, 2022.

Yang-Baxter elements & a new proof of homological stability for the mapping class group of surfaces