Double quasi-Poisson brackets on associative algebras with involutive anti-automorphisms induce quasi-Poisson structures on twisted representation spaces over arbitrary semisimple bases, with applications to twisted quiver varieties and Hopf algebras with Fox pairings.
Preprint,arXiv:1804.09566
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Introduces K-framings, based K-framings and relative K-framings on surfaces and generalizes the Johnson quadratic form-spin structure correspondence to arbitrary commutative rings K, with a bijection to twisted cocycles of the mapping class group.
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.
Equivalences between moperads of parenthesized braids with frozen strand and chord diagrams generate families of genus zero KV solutions from a single classical one, with GT module groups acting compatibly, and a symmetric KV solution induces a map factoring through chord diagrams iff the associator
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Quasi-Poisson varieties from double quasi-Poisson algebras in types $B,C,D$
Double quasi-Poisson brackets on associative algebras with involutive anti-automorphisms induce quasi-Poisson structures on twisted representation spaces over arbitrary semisimple bases, with applications to twisted quiver varieties and Hopf algebras with Fox pairings.
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$\mathbb{K}$-framings and $\mathbb{K}$-quadratic forms on surfaces
Introduces K-framings, based K-framings and relative K-framings on surfaces and generalizes the Johnson quadratic form-spin structure correspondence to arbitrary commutative rings K, with a bijection to twisted cocycles of the mapping class group.
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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.
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Genus Zero Kashiwara-Vergne Solutions from Braids
Equivalences between moperads of parenthesized braids with frozen strand and chord diagrams generate families of genus zero KV solutions from a single classical one, with GT module groups acting compatibly, and a symmetric KV solution induces a map factoring through chord diagrams iff the associator