Mapping class group actions from Hopf monoids

Abstract: We show that pivotal Hopf monoids in symmetric monoidal categories give rise to actions of mapping class groups of oriented surfaces with boundary components. These mapping class group actions are associated with edge slides in embedded ribbon graphs that generalise chord slides in chord diagrams. They can be described simply and concretely in terms of generating Dehn twists. Under certain assumptions on the symmetric monoidal category and the Hopf monoid, they induce actions of mapping class groups of closed surfaces.

geometric topology

Audience: researchers in the topic

( paper )

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[K-OS] Knot online seminar

Series comments: Description: Seminar on knot theory and low dimensional topology

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