2
votes
2answers
277 views

Origin of the name “Torelli group”

The genus $g$ Torelli group $I_g$ is the kernel of the action of the mapping class group of a genus $g$ surface on the first homology group of the surface. The first paper I am aware of that uses the ...
6
votes
0answers
156 views

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 ...
4
votes
2answers
265 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 ...
23
votes
8answers
2k 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 ...
6
votes
3answers
615 views

Classification of Platonic solids

My question is very basic: where can I find a complete (and hopefully self-contained) proof of the classification of Platonic solids? In all the references that I found, they use Euler's formula ...
7
votes
0answers
212 views

What is the historical connection between Zeeman's twist spinning and Fox's Examples?

Both Ralph Fox and (at that time, yet to be knighted) Sir Christopher Zeeman attended the 1961 Georgia topology conference. Fox's paper from that conference was his seminal work, "A Quick Trip through ...
5
votes
1answer
360 views

Historical question: fiber bundles

I am sorry if this question is too trivial but I couldn't find the answer. Who did first classify topological principal $G$-bundles for some topological group $G$? So, I mean that equivalence ...
3
votes
1answer
492 views

What does the 'V' in 'V-manifold' stand for?

The story of how the name 'orbifold' came about is pretty well-documented, but I can't find any explanation as to why Satake originally named orbifolds 'V-manifolds'. The 'manifold' part is clear ...
5
votes
1answer
413 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 ...
3
votes
1answer
386 views

Klein Bottle exception to the Heawood Conjecture [duplicate]

Possible Duplicate: The Klein bottle and the Heawood Conjecture It is well known that the Heawood Conjecture states that the bound for the number of colours which are sufficient to colour a ...
4
votes
1answer
304 views

Residual finiteness of fundamental groups of surfaces.

What is a simple way to prove that for any compact two-dimensional surface $S$ and an element $g$ in $\mathbb \pi_1(S)$ there exists a finite index normal subgroup $\Gamma\subset \pi_1(S)$ such that ...
47
votes
3answers
6k views

The story about Milnor proving the Fáry-Milnor theorem

This question is similar to a previous one about "urban legends", but not the same. It is established that Milnor proved the Fáry-Milnor theorem as an undergraduate at Princeton. For the record, ...