Mapping class group actions from Hopf monoids and ribbon graphs

Meusburger C, Voß T (2021)


Publication Type: Journal article

Publication year: 2021

Journal

Book Volume: 12

Pages Range: 507-591

Journal Issue: 3

DOI: 10.4171/QT/158

Abstract

We show that any pivotal Hopf monoid H in a symmetric monoidal category C gives rise to actions of mapping class groups of oriented surfaces of genus g >= 1 with n >= 1 boundary components. These mapping class group actions are given by group homomorphisms into the group of automorphisms of certain Yetter-Drinfeld modules over H. They are associated with edge slides in embedded ribbon graphs that generalise chord slides in chord diagrams. We give a concrete description of these mapping class group actions in terms of generating Dehn twists and defining relations. For the case where C is finitely complete and cocomplete, we also obtain actions of mapping class groups of closed surfaces by imposing invariance and coinvariance under the Yetter-Drinfeld module structure.

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How to cite

APA:

Meusburger, C., & Voß, T. (2021). Mapping class group actions from Hopf monoids and ribbon graphs. Quantum Topology, 12(3), 507-591. https://dx.doi.org/10.4171/QT/158

MLA:

Meusburger, Cathérine, and Thomas Voß. "Mapping class group actions from Hopf monoids and ribbon graphs." Quantum Topology 12.3 (2021): 507-591.

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