Related papers: The string topology BV algebra, Hochschild cohomol…

We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a 1-connected closed manifold M. We prove that the loop homology of M is isomorphic to the…

We construct a Batalin-Vilkovisky (BV) algebra on moduli spaces of Riemann surfaces. This algebra is background independent in that it makes no reference to a state space of a conformal field theory. Conformal theories define a homomorphism…

We describe two major string topology operations, the Chas-Sullivan product and the Goresky-Hingston coproduct, from geometric and algebraic perspectives. The geometric construction uses Thom-Pontrjagin intersection theory while the…

The free loops space $\Lambda X$ of a space $X$ has become an important object of study particularly in the case when $X$ is a manifold.The study of free loop spaces is motivated in particular by two main examples. The first is their…

Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra -- the…

Topological Hochschild homology (THH) is an invariant of ring spectra developed by B\"okstedt. In recent years many equivariant analogues to THH have emerged. One example is twisted THH which is an invariant of $C_n$-equivariant ring…

Given a closed manifold $M$. We give an algebraic model for the Chas-Sullivan product and the Goresky-Hingston coproduct. In the simply-connected case, this admits a particularly nice description in terms of a Poincar\'e duality model of…

We construct and study an algebraic analogue of the loop coproduct in string topology, also known as the Goresky-Hingston coproduct. Our algebraic setup, which under this analogy takes the place of the complex of chains on the free loop…

We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f: X->BF, where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of…

The purpose of this article is to embed the string topology bracket developed by Chas-Sullivan and Menichi on negative cyclic cohomology groups as well as the dual bracket found by de Thanhoffer de Voelcsey-Van den Bergh on negative cyclic…

We describe the Gerstenhaber algebra structure on the Hochschild cohomology HH*$(A)$ when $A$ is a quadratic string algebra. First we compute the Hochschild cohomology groups using Barzdell's resolution and we describe generators of these…

Let M be a connected, simply connected, closed and oriented manifold, and G a finite group acting on M by orientation preserving diffeomorphisms. In this paper we show an explicit ring isomorphism between the orbifold string topology of the…

In this paper, we discuss Hochschild chain models for some of the string topology operations. We use these models to simplify the proofs and computations of some of the results in string topology. Along the way we also make some new…

We show that the graded commutative ring structure of the Hochschild cohomology HH*(A) is trivial in case A is a triangular quadratic string algebra. Moreover, in case A isgentle, the Lie algebra structure on HH*(A) is also trivial.

The chain gravity properad introduced earlier by the author acts on the cyclic Hochschild of any cyclic $A_\infty$ algebra equipped with a scalar product of degree $-d$. In particular, it acts on the cyclic Hochschild complex of any…

We show that the reduced Hochschild homology of a DG open Frobenius algebra has the natural structure of a Batalin-Vilkovisky coalgebra, and the reduced cyclic homology has the natural structure of a gravity coalgebra. This gives an…

F\'{e}lix and Thomas developed string topology of Chas and Sullivan on simply-connected Gorenstein spaces. In this paper, we prove that the degree shifted homology of the free loop space of a simply-connected ${\mathbb Q}$-Gorenstein space…

In this paper, we define the singular Hochschild cohomology groups $HH_{sg}^i(A, A)$ of an associative $k$-algebra $A$ as morphisms from $A$ to $A[i]$ in the singular category $D_{sg}(A\otimes_k A^{op})$ for $i\in \mathbb{Z}$. We prove that…

Let $M$ be a compact oriented $d$-dimensional smooth manifold and $X$ a topological space. Chas and Sullivan \cite{Chas-Sullivan:stringtop} have defined a structure of Batalin-Vilkovisky algebra on $\mathbb{H}_*(LM):=H_{*+d}(LM)$. Getzler…

Given a differential graded (dg) symmetric Frobenius algebra $A$ we construct an unbounded complex $\mathcal{D}^{*}(A,A)$, called the Tate-Hochschild complex, which arises as a totalization of a double complex having Hochschild chains as…