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This point of view is based on the talk of Joel Villatoro titled paths in Lie-Rinehart algebras. I may be misunderstanding what Joel Villatoro is mentioning. Correct me if I am saying something wrong. …

I heard the idea of a Lie-Rinehart algebra first time from an algebraist. I noticed there is a similarity between description of Lie algebroid on a manifold and the algebraic notion of Lie-Rinehart al …

Lie's third theorem : Given any finite dimensional Lie algebra $\mathfrak{g}$, there exists a Lie group $G$ whose Lie algebra is equal to $\mathfrak{g}$. In one of the talks, speaker mentions that thi …

For someone who is new to Lie $\infty$-algebras, the title looks confusing. This is how Lie $\infty$-algebras are commonly described, for example, see What is a homotopy between $L_\infty$-algebra mor …

I am trying to see some standard examples of Lie $2$-algebroids. The first entry in Google search takes me to Madeleine Jotz Lean's work Lie 2-algebroids and matched pairs of 2-representations — a geo …

I am trying to write my understanding of "Lie algebroid of derivations $\mathcal{D}(E)\rightarrow M$ associated to a vector bundle $E\rightarrow M$". Given a vector bundle $E\rightarrow M$, we want to …

I am reading "Differential operators and actions of Lie algebroids" by Kosmann-Schwarzbach and Mackenzie. There is some confusion regarding the terminology. Let $E\rightarrow M$ be a vector bundle. A …

I am trying to see if there is any existing cohomology theory for Dirac manifolds. For the case of poisson manifolds, we have the notion of Poisson cohomology. For a manifold $M$, one can consider the …

Even though we may not be able to associate a Lie algebroid with a singular foliation, we can associate a Lie $\infty$-algebroid with a singular foliation (satisfying certain not so strange conditions …

I am learning about "derived manifolds" from talks of Ping Xu in Higher Structures in Geometry and Mathematical Physics. As far as I understand, one of the main philosophy behind the introduction of d …

Question is as mentioned in the title: Are there any introductory notes on deformation theory that are easier to read for differential geometers? I am learning about differential graded Lie algebras ( …

A foliation on a manifold $M$ can be seen as a sub bundle of the tangent bundle $\mathcal{F}\subseteq TM$ that is closed under Lie bracket of vector fields. One can think of foliation as a Lie algebro …

Equivariant geometry studies "manifolds" with an extra structure $G\times M\rightarrow M$. Representation theory studies "Lie algebroids" with an extra structure $\Gamma(M,A)\times \Gamma(M,E)\rightar …

Kirill Mackenzie has a book on the general theory of Lie groupoids and Lie algebroids. Is there such a reference for the general theory of Lie $\infty$-groupoids and Lie $\infty$-algebroids; that cove …

The question is as in the title. (What are some of the) are there any applications of Homotopical algebra (in the context of Quillen’s book “Homotopical algebra”) in better understanding (or developi …