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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

5 votes

Terminology introduced in recent years with more than one meaning

The word “topological stack” has at least three usages: A stack $\mathcal{D}\rightarrow \text{Top}$ is said to be a topological stack if there is a a morphism of stacks $p: \underline{M}\rightarrow …
5 votes
5 answers
2k views

Terminology introduced in recent years with more than one meaning

Suppose a term(inology) is recently (in last 20 years) introduced in research mathematics. It might happen that some one who wish to use it, in the same area of research, for different purposes or se …
79 votes
9 answers
21k views

Results that are widely accepted but no proof has appeared

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. …
2 votes
2 answers
214 views

Measuring failure of a setup to preserve some structure giving interesting notions

I am looking for some examples of failure of some structures giving interesting notions. For example, we have the following situation: Let $P(M,G)$ be a principal bundle. Let $\Gamma\subseteq TP$ be …
1 vote

Examples of great mathematical writing

I want to mention two papers (related). The very famous Complex analytic connections in fibre bundles by Michael Atiyah. The not so famous The Atiyah bundle and connections on a principal bundle by …
62 votes

LaTeX tricks that save time in typesetting

In case you want to use tikzcd to draw diagrams this tikzcd editor saves lot of time. \begin{tikzcd} & & A \arrow[rr] \arrow[lld] \arrow[dd] & & V \arrow[d] & \arrow[dd] \\ & V \arrow[dd] \arrow …
18 votes

Old books you would like to have reprinted with high-quality typesetting

A general theory of Fibre spaces with Structure sheaf by Alexandre Grothendieck
9 votes

Old books you would like to have reprinted with high-quality typesetting

Curvature and Characteristic classes by J. L. Dupont.
3 votes
0 answers
468 views

Applications of Ambrose-Singer theorem on holonomy

I am planning to introduce to a group of Graduate students the notion of connections on Principal bundle, curvature of connection, Holonomy. I want to conclude with the statement of Ambrose-Singer t …
8 votes
2 answers
3k views

What does reduction of structure group of principal bundle say?

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