My question is very naive maybe, I don't have a deep knowledge about string topology. I wanted to ask (explanation or a reference) for the geometric interpretation of free loop sp …

Chas and Sullivan constructed in 1999 a Batalin-Vilkovisky algebra structure on the shifted homology of the loop space of a manifold: $\mathbb{H}_*(LM) := H_{*+d}(LM;\mathbb{Q})$. …

Let $C$ be an arbitrary algebra (more generally, a linear 1-category). The following structures are well-known: A degree-0 product on the Hochschild cohomology $HH^*(C)$ $$ HH^* …

I am reading Veronique Godin's famous article "Higher string topology operations" (http://arxiv.org/abs/0711.4859) that demonstrates that the string topology operations on $(H_\bul …

Recall that a ribbon graph is a graph with a cyclic ordering at each vertex and such that each vertex has valence greater than or equal to 3. This cyclic ordering exactly gives one …

After reading Cohen and Voronov's notes on string topology, one can find the following construction: Suppose we have a topological space $X$ with continuous action of $S^1$. This m …

String topology studies the algebraic structure of the homology of the free loop space $LM = Map(S^1,M)$ of a oriented closed manifold. One aspect of this structure is that the pai …

I recently read the original paper by Chas-Sullivan on string topology, in which they introduce some operations on homology of free loopspace LM, where M is a compact oriented mani …

For cohomology with coefficients in a field $F$ the map $H^\cdot(X;F) \otimes H^\cdot(Y;F) \to H^\cdot(X \times Y;F)$ of the Kunneth theorem is an isomorphism of algebras over $F$. …

Kevin Costello's article on the Gromov-Witten potential associated to a TCFT constructs for each TCFT, i.e. a functor from chains on Riemann surfaces with boundary to chain complex …

In her article Higher string topology operations, Godin in particular construct for each surface with $n$ incoming and $m \geq 1$ outgoing boundary circles an operation $H_\ast(BMo …