bio  website  math.univmontp2.fr/~calaque 

location  Montpellier  
age  35  
visits  member for  4 years, 2 months 
seen  Aug 20 at 5:32  
stats  profile views  3,164 
I am interested in Mathematical Physics, Algebra, and Geometry.
11h

awarded  Necromancer 
Jul 2 
awarded  Curious 
Jun 23 
awarded  Yearling 
Jan 24 
awarded  Nice Answer 
Jan 8 
comment 
What does “variété à coins” translate to in English?
Yes. It translates to "manifold with corners". 
Dec 19 
answered  Are $(\infty,1)$categories $A_\infty$ categories? 
Nov 8 
comment 
Is there a “by hand” proof on the symmetry of the Atiyah class of $TX$?
Well, there is a byhand (and differential geometric) proof in the paper of Roberts and Willerton that you cite. It is not on page 29 (where they explain Kapranov's proof) but earlier on page 14. They do it very explicitely (see my answer below). 
Oct 26 
comment 
About the Lie algebra of polyvector fields
You might want to have a look at people.su.se/~merku/Papers/Automorphv4_0.pdf 
Oct 14 
awarded  Revival 
Oct 14 
comment 
What is the relation between the Lie bracket on $TX$ as commutator and that coming from the Atiyah class?
Caldararu's conjecture involves Hochschild cochains too. Cochains can be viewd as distributions on the derived loop space, their cupproduct being the convolution product of distributions. 
Oct 14 
revised 
Is there a “by hand” proof on the symmetry of the Atiyah class of $TX$?
added details about Proposition 2.2 in RobertsWilerton. 
Oct 13 
revised 
Is there a “by hand” proof on the symmetry of the Atiyah class of $TX$?
added 203 characters in body 
Oct 12 
answered  What's the relation between the heat kernel proof of the index theorem and deformation quantization? 
Oct 12 
answered  Is there a “by hand” proof on the symmetry of the Atiyah class of $TX$? 
Oct 9 
comment 
What is the relation between the Lie bracket on $TX$ as commutator and that coming from the Atiyah class?
Another way to phrase this is to say that $X_1$ is the homotopy fiber of the morphism $X\to X_0$ of derived groupoid schemes over $X$ ($X$ is the trivial groupoid). Passing to Lie algebroids we get that the Lie algebroid of $X_1$ is the homotopy fiber of $0\to TX$ in dg Lie algebroid over $X$. Its underlying sheaf is then $TX[1]$. 
Oct 9 
comment 
What is the relation between the Lie bracket on $TX$ as commutator and that coming from the Atiyah class?
$\Omega_0(TX)$ is defined to be the selfhomotopy fiber product of $0\to TX$. $\Omega_0^n$ just means that we iterate this operation $n$ times. Doing this in the category of dg Lie algebroids over $X$ (see Vezzosi's recent note for the description of a model structure on it) we get that $\Omega_0(TX)$ is a group bject in dg Lie algebroids, and hence must be a Lie algebra (I don't know any reference for this last part). 
Oct 8 
revised 
What is the relation between the Lie bracket on $TX$ as commutator and that coming from the Atiyah class?
rephrasing 
Oct 8 
revised 
Could we extend the Atiyah class to the sheaf of polyvector fields to get a Poisson bracket?
objecta > object 
Oct 5 
answered  What is the relation between the Lie bracket on $TX$ as commutator and that coming from the Atiyah class? 
Oct 5 
revised 
Could we extend the Atiyah class to the sheaf of polyvector fields to get a Poisson bracket?
edited body 