Multi-oriented props and homotopy algebras with branes

in Letters in Mathematical Physics (2020), 110

We introduce a new category of differential graded {\em multi-oriented}\, props whose representations (called homotopy algebras with branes) in a graded vector space require a choice of a collection of $k ... [more ▼]

We introduce a new category of differential graded {\em multi-oriented}\, props whose representations (called homotopy algebras with branes) in a graded vector space require a choice of a collection of $k$ linear subspaces in that space, $k$ being the number of extra directions (if $k=0$ this structure recovers an ordinary prop); symplectic vector spaces equipped with $k$ Lagrangian subspaces play a distinguished role in this theory. Manin triples is a classical example of an algebraic structure (concretely, a Lie bialgebra structure) given in terms of a vector space and its subspace; in the context of this paper Manin triples are precisely symplectic Lagrangian representations of the {\em 2-oriented} generalization of the classical operad of Lie algebras. In a sense, the theory of multi-oriented props provides us with a far reaching strong homotopy generalization of Manin triples type constructions. [less ▲]

Differentials on graph complexes II: hairy graphs

in Letters in Mathematical Physics (2017), 107(10), 17811797

We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging ... [more ▼]

We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging to zero whose first pages contain the hairy graph cohomology. Our results yield a way to construct many nonzero hairy graph cohomology classes out of (known) non-hairy classes by studying the cancellations in those sequences. This provide a first glimpse at the tentative global structure of the hairy graph cohomology. [less ▲]

On twisted N= 2 5D super Yang-Mills theory

in Letters in Mathematical Physics (2016), 106(1), 127

Warped products and Yang-Mills equations on noncommutative spaces

in Letters in Mathematical Physics (2015), 105(2), 221243

Deformations of coisotropic submanifolds for fibrewise entire Poisson structures

in Letters in Mathematical Physics (2013), 103(7), 777-791

We show that deformations of a coisotropic submanifold inside a fibrewise entire Poisson manifold are controlled by the L-infinity-algebra introduced by Oh-Park (for symplectic manifolds) and Cattaneo ... [more ▼]

We show that deformations of a coisotropic submanifold inside a fibrewise entire Poisson manifold are controlled by the L-infinity-algebra introduced by Oh-Park (for symplectic manifolds) and Cattaneo-Felder. In the symplectic case, we recover results previously obtained by Oh-Park. Moreover we consider the extended deformation problem and prove its obstructedness. [less ▲]

Equivariant symbol calculus for differential operators acting on forms

in Letters in Mathematical Physics (2002), 62(3), 219-232

String branchings on complex tori and algebraic representations of generalized Krichever-Novikov algebras

in Letters in Mathematical Physics (1992), 26(1), 23-32

Krichever-Novikov algebras for more than two points: explicit generators

in Letters in Mathematical Physics (1990), 19(4), 327-336