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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. …

What are the occurrences of the notion of a stack outside algebraic geometry, differential geometry, and general topology? In most of the references, the introduction of the notion of a stack takes …

I was reading David Carchedi's answer for a question on Grothendieck topology for a non-small category. It "reads" like people "choose" if they allow manifolds to be Hausdorff and/or second countable. …

I am looking for some references related to gerbes and their differential geometry. Almost every article I have seen that is related to gerbes there is a common reference that is Giraud's book Cohomo …

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 ( …

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 …

Angelo Vistoli in the notes Notes on Grothendieck topologies, fibered categories and descent theory starts the section of category theory with the following note: We will not distinguish between s …

Given a principal $G$ bundle $P(M,G)$ and a manifold $F$ with an action of $G$ on it from left, we construct a fiber bundle over $M$ with fiber $F$ and call this the associated fiber bundle for $P(M,G …

Consider the category of smooth manifolds $\text{Man}$. I quote from n-lab page: Manifolds are fantastic spaces. It’s a pity that there aren’t more of them. I understand that this category $\text{Ma …

Given a Lie group $G$, we have a Lie groupoid $(G\rightrightarrows *)$ and stack $BG=B\mathcal{G}$ of principal $G$ bundles. Given a smooth manifold $M$, we have Lie groupoid $(M\rightrightarrows M …

I am trying to understand about Lie groupoids but not able to get feeling for what it actually is. So, question here is, What are Lie groupoids? How similar are they to Lie groups, Groupoids and …

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SO{SO}$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 …

In Introduction to Differentiable Stacks Gregory Ginot defines a $G$-gerbe as the following. Let $G$ be a Lie group. A $G$-gerbe over a stack $\mathcal{C}$ is a gerbe over stack $\mathcal{D}\righ …

Let $G$ be a Lie group and $\pi:E_G\rightarrow M $ be a principal $G$-bundle. I have seen in many places that a connection on $(E_G,M,G)$ is a splitting of the Atiyah sequence $$ 0\rightarrow \text …

Consider a manifold $M$. Then, we have the notion of differential forms on $M$ and complex associated to that, denoted by $$\cdots\rightarrow \Omega^{k-1}(M)\rightarrow \Omega^k(M)\rightarrow \Omega^{ …