3,860 reputation
1942
bio website math.univ-montp2.fr/~calaque
location Montpellier
age 35
visits member for 4 years, 4 months
seen Oct 8 at 13:17

I am interested in Mathematical Physics, Algebra, and Geometry.


Oct
5
awarded  Nice Answer
Sep
30
awarded  Explainer
Aug
29
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 by-hand (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/Automorph-v4_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 cup-product 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 Roberts-Wilerton.
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 self-homotopy 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 poly-vector fields to get a Poisson bracket?
objecta -> object