Direct construction of higher-genus KV associators from Gonzalez-Drinfeld associators via generalization of Massuyeau's genus-0 proof, determining framings with genus-1 restrictions.
Surface framed braids
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abstract
In this paper we introduce the framed pure braid group on $n$ strands of an oriented surface, a topological generalisation of the pure braid group $P_n$. We give different equivalents definitions for framed pure braid groups and we study exact sequences relating these groups with other generalisations of $P_n$, usually called surface pure braid groups. The notion of surface framed braid groups is also introduced.
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math.QA 1years
2025 1verdicts
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Drinfeld associators and Kashiwara-Vergne associators in higher genera
Direct construction of higher-genus KV associators from Gonzalez-Drinfeld associators via generalization of Massuyeau's genus-0 proof, determining framings with genus-1 restrictions.