All Questions
7 questions
15
votes
1
answer
877
views
$\mathbb{R}^3$ as the union of disjoint circles
In the question Covering the space by disjoint unit circles
the following result is attributed to Sierpinski.
Theorem. The Euclidean space $\mathbb{R}^3$ is a union of nondegenerate disjoint circles....
- 12.3k
14
votes
5
answers
1k
views
History of the notion of $(G,X)$-structure
I'm currently searching for sources and historical basis on the notion of $(G,X)$-structure as it appears in Thurston's work.
So far, it appears that he was the first to set it. Many mathematicans ...
- 403
4
votes
1
answer
1k
views
Cap product à la Poincaré
Recently, it became apparent to me that I was not the only one who always first thought in terms of cap product before actually computing a cup product. There is no denying this is evil, but I found ...
- 4,432
7
votes
0
answers
448
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Reference Request: Topological h-cobordism theorem in higher dimensions
I think this question on math.stackexchange is more appropriate on mathoverflow. Correct me, if you don't think so.
The h-cobordism theorem is true in the topological and in the smooth category in ...
- 71
5
votes
3
answers
593
views
Who first used the cross-ratio to describe shapes in hyperbolic geometry?
I was reading this Wikipedia article today:https://en.wikipedia.org/wiki/Shape#Similarity_classes
and I realized that it strongly resembles the use of coss-ratios as "shape parameters" in hyperbolic ...
- 3,359
39
votes
10
answers
4k
views
Are there some other notions of "curvature" which measure how space curves?
I am learning differential geometry and have a few questions on curvature. -- Background:
Gauss invented "Gauss curvature" to measure how surface curves.
Riemann gives an ingenious generalization of ...
9
votes
1
answer
816
views
Who invented the Morse-Bott-complex?
In the "Morse-Bott theory and equivariant cohomology" paper by D.M. Austin and P.J. Braam, the authors introduce the Morse-Bott-complex to calculate the de-Rham-cohomology of a compact manifold (using ...
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