bio | website | math.univ-montp2.fr/~calaque |
---|---|---|
location | Montpellier | |
age | 35 | |
visits | member for | 4 years, 4 months |
seen | Oct 8 at 13:17 | |
stats | profile views | 3,198 |
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 |