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Let $M$ be a manifold. Let $G$ be a Lie group and $\mathfrak{g}$ be its Lie algebra. Let $P(M,G)$ be a principal bundle. Recall that, a connection on $P(M,G)$ is a distribution $\mathcal{H}\subseteq …

Let $P(M,G)$ be a principal bundle. Giving a connection on $P(M,G)$ means two equivalent things. One as an assignment of subspace of $T_pP$ for each $p\in P$ and another as a $\mathfrak{g}$ valued $1$ …

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 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 …

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. …

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 …

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 …

I am reading "Some notes on Differentiable stacks" by J. Heinloth. In that paper, the notion of quotient stack is defined as follows. Let $G$ be a Lie group action on a manifold $X$ (left action). We …

I am reading Orbifolds as stacks? Given Lie groupoids $\mathcal{G}$ and $\mathcal{H}$ there is a notion of what is called a bibundle from $\mathcal{G}$ to $\mathcal{H}$ which is supposed to be a agene …

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 …

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SO{SO}$Let $G$ be a Lie group and $\pi:P\rightarrow M$ be a principal $G$ bundle. The notion of reduction of structure group is standard but I will rec …

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 …

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 …

I am trying to understand about principal G bundle given a Lie group $G$. For that, I started with the action of Lie groups on manifold $M$ and convinced myself that if the action is smooth, proper, a …

The background of this question is the talk given by Kevin Buzzard. I could not find the slides of that talk. The slides of another talk given by Kevin Buzzard along the same theme are available here. …