Related papers: String topology via the coHochschild complex and l…

In the paper we describe complexes whose homologies are naturally isomorphic to the first term of the Vassiliev spectral sequence computing (co)homology of the spaces of long knots in R^d, d>=3. The first term of the Vassiliev spectral…

The Hochschild cohomology of a tensor product of algebras is isomorphic to a graded tensor product of Hochschild cohomology algebras, as a Gerstenhaber algebra. A similar result holds when the tensor product is twisted by a bicharacter. We…

We construct an equivalence of $E_{2}$ algebras between two models for the Thom spectrum of the free loop space that are related by derived Koszul duality. To do this, we describe the functoriality and invariance properties of topological…

We study the topologically twisted string theory on the general back-ground $AdS_3\times {\cal N}$ which is compatible with the world-sheet N=2 superconformal symmetry and is extensively discussed in the recent works (hep-th/9904024,…

We introduce BV-algebra structures on the homology of the space of framed long knots in $\mathbb{R}^n$ in two ways. The first one is given in a similar fashion to Chas-Sullivan's string topology. The second one is defined on the Hochschild…

These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…

We combine Sullivan models from rational homotopy theory with Stasheff's $L_\infty$-algebras to describe a duality in string theory. Namely, what in string theory is known as topological T-duality between $K^0$-cocycles in type IIA string…

I present a new class of topological string theories, and discuss them in two dimensions as candidates for the string description of large-$N$ QCD. The starting point is a new class of topological sigma models, whose path integral is…

We study properties of differential graded (dg) operads modulo weak equivalences, that is, modulo the relation given by the existence of a chain of dg operad maps inducing a homology isomorphism. This approach, naturally arising in string…

We investigate how topological entanglement of Chern-Simons theory is captured in a string theoretic realization. Our explorations are motivated by a desire to understand how quantum entanglement of low energy open string degrees of freedom…

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…

The topological Hochschild homology $THH(A)$ of an orthogonal ring spectrum $A$ can be defined by evaluating the cyclic bar construction on $A$ or by applying B\"okstedt's original definition of $THH$ to $A$. In this paper, we construct a…

The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links…

Given $f: M \to N$ a homotopy equivalence of compact manifolds with boundary, we use a construction of Geoghegan and Nicas to define its Reidemeister trace $[T] \in \pi_1^{st}(\mathcal{L} N, N)$. We realize the Goresky-Hingston coproduct as…

We describe an algebraic chain level construction that models the passage from an arbitrary topological space to its free loop space. The input of the construction is a categorical coalgebra, i.e. a curved coalgebra satisfying certain…

For an $\E$-ring spectrum $R$ and a map $f:X\to Pic(R)$ of spaces, the Thom spectrum $\T f$ is a comodule over $R\otimes\Si X$. In this parper we study the topological coHochschild homology of $R\otimes\Si X$ with coefficient $\T f$. More…

We construct a Frobenius algebra structure on the Hochschild cochains of a group ring k[G] that extends the known structure of a <1, 2> topological quantum field theory on HH^0(k[G]; k[G]), k a field and G a finite group. The convolution…

In previous work with Schoenfeld, we considered a string-type chain complex of curves on surfaces, with differential given by resolving crossings, and computed the homology of this complex for discs. In this paper we consider the…

We give an introductory review of topological strings and their application to various aspects of superstrings and supersymmetric gauge theories. This review includes developing the necessary mathematical background for topological strings,…

Local Hochschild, cyclic Homology and K-theory were introduced by N. Teleman in [10] with the purpose of unifying different settings of the index theorem. This paper is one of the research topics announced in [10], {\S}10. The definition of…