The string-topology tag has no usage guidance.

**11**

votes

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329 views

### Gerstenhaber conjecture for free loop space

I- Is the following statement still a conjecture see this article ?
Conjecture (?)
Let $M$ be a simply connected compact oriented $d$-manifold (smooth), then $HH^{\ast}(C^{\ast}(M))$ the Hochschild ...

**3**

votes

**1**answer

116 views

### Hochschild chain model for the evaluation map at half

Let M be a manifold and $\Lambda(M)$ its free loop space, $A= C^*(M)$ denotes the cochain algebra of $M$. We know that Hochschild chain model for the evaluation $ ev_0: \Lambda(M) \rightarrow M$ is ...

**2**

votes

**1**answer

218 views

### Are there analogs of String Homology structure in cyclic homology?

I was reading John D.S. Jones' paper "Cyclic homology and equivariant homology" where he introduces a variant of cyclic homology that is isomorphic (as modules over the ring $K[u]$) to equivariant ...

**0**

votes

**0**answers

135 views

### loop space homology and lens spaces

Is the homology of free loop space of lens spaces known?
Thanks in advance for your help.

**6**

votes

**3**answers

428 views

### String topology for a Lie group

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 space (continues maps) ...

**9**

votes

**2**answers

745 views

### Relation between Gerstenhaber bracket and Connes differential

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^*(C) \otimes HH^*(C) \...

**9**

votes

**1**answer

634 views

### Pull-push in Godin's HCFT for string topology

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_\bullet(L X), H_\bullet(...

**13**

votes

**3**answers

720 views

### Are there graph models for other moduli spaces?

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 the information to ...

**3**

votes

**0**answers

384 views

### Does a Dehn twist in the mapping class group of an cobordism give a BV-operator in string topology?

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(BMod(S);det^{\otimes d})...

**10**

votes

**1**answer

610 views

### What does this naive attempt at $S^1$-equivariant homology describe?

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 means we have a map $\...

**5**

votes

**1**answer

596 views

### Can string topology be a open-closed TCFT with the full set of branes?

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 pair $(H_\ast(LM;\...

**3**

votes

**1**answer

669 views

### What is the Gromov-Witten potential associated to String Topology?

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 ...

**24**

votes

**6**answers

2k views

### Applications of string topology structure

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

**8**

votes

**2**answers

1k views

### Chas-Sullivan string topology

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 manifold, giving it the ...

**8**

votes

**2**answers

595 views

### Is the cohomology of a topological operad a cooperad?

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 $F$. I am correct in ...