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Results tagged with big-list
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user 118688
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.
8
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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 …
79
votes
9
answers
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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. …
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5
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5
answers
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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 …
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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 …
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votes
2
answers
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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 …
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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 …
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62
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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 …
CommunityBot
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Old books you would like to have reprinted with high-quality typesetting
A general theory of Fibre spaces with Structure sheaf by Alexandre Grothendieck
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Old books you would like to have reprinted with high-quality typesetting
Curvature and Characteristic classes by J. L. Dupont.
- 6,023
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0
answers
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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 …
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