Thomas Tradler

Equivariant Holonomy for Bundles and Abelian Gerbes

This paper generalizes Bismut’s equivariant Chern character to the setting of abelian gerbes. In particular, associated to an abelian gerbe with connection, an equivariantly closed differential form is constructed on the space of maps of a torus into the manifold. These constructions are made explicit using a new local version of the higher Hochschild complex, resulting in differential forms given by iterated integrals. Connections to two dimensional topological field theories are indicated. Similarly, this local higher Hochschild complex is used to calculate the 2-holonomy of an abelian gerbe along any closed oriented surface, as well as the derivative of 2-holonomy, which in the case of a torus fits into a sequence of higher holonomies and their differentials.

Algebraic string bracket as a Poisson bracket

In this paper we construct a Lie algebra representation of the algebraic string bracket on negative cyclic cohomology of an associative algebra with appropriate duality. This is a generalized algebraic version of the main theorem of [AZ] which extends Goldmans results using string topology operations.The main result can be applied to the de Rham complex of a smooth manifold as well as the Dolbeault resolution of the endomorphisms of a holomorphic bundle on a Calabi-Yau manifold.

The combinatorics of directed planar trees

We give a geometric realization of the polyhedra governed by the structure of associative algebras with co-inner products, or more precisely, governed by directed planar trees. Our explicit realization of these polyhedra, which include the associahedra in a special case, shows in particular that these polyhedra are homeomorphic to balls. We also calculate the number of vertices of the lowest generalized associahedra, giving appropriate generalizations of the Catalan numbers.

Tensor products of _{∞}-algebras with homotopy inner products

We show that the tensor product of two cyclic

On the cyclic Deligne conjecture

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Higher Hochschild Homology, Topological Chiral Homology and Factorization Algebras

-algebras is, in general, not a cyclic

The BV Algebra on Hochschild Cohomology Induced by Infinity Inner Products

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Infinity structure of Poincaré duality spaces

-algebra, but an

Algebraic string operations

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A CHEN MODEL FOR MAPPING SPACES AND THE SURFACE PRODUCT

-algebra with homotopy inner product. More precisely, we construct an explicit combinatorial diagonal on the pairahedra, which are contractible polytopes controlling the combinatorial structure of an