All Questions
9 questions
147
votes
21
answers
23k
views
Are there examples of non-orientable manifolds in nature?
Whilst browsing through Marcel Berger's book "A Panoramic View of Riemannian Geometry" and thinking about the Klein bottle, I came across the sentence:
"The unorientable surfaces are never discussed ...
- 502
43
votes
11
answers
15k
views
Open questions in Riemannian geometry
What are some major open problems in Riemannian Geometry? I tried googling it, but couldn't find any resources.
- 5,407
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.
...
- 751
4
votes
0
answers
421
views
What are your common strategies/remedies when your new theory/idea stuck in most cases?
Sorry if this is not a suitable post for MO.
Sometimes after reading the origin of a theory/idea in differential topology I put myself in the shoes of that mathematician and ask myself, Did you do the ...
- 4,195
22
votes
1
answer
3k
views
What is so special about Chern's way of teaching?
First of all sorry for this non-research post.
I was watching Jeffrey Blitz Lucky documentary movie and it was interesting to me that a winner of Lottery was a math Ph.D. from Berkeley.
In the movie ...
- 188k
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 ...
- 6,023
27
votes
10
answers
2k
views
Examples of Kan extensions, adjunctions, and (co)monads in analysis, Lie theory, and differential geometry?
In introductory texts on category theory, it seems like the majority of examples come from algebraic topology, algebra, and logic.
What are some good examples of Kan extensions, adjunctions, and (co)...
- 6,025
4
votes
0
answers
653
views
Research topics in Curves and Surfaces [closed]
I advance that I'm not a mathematician but I'm an undergraduate student of mathematics. In my courses at university I have studied a bit of Differential Geometry, in particoular differential geometry ...
- 1,252
16
votes
3
answers
3k
views
group of diffeomorphisms of a manifold
How much has been the group of diffeomorphisms of a manifold " been studied.
I got this information from wiki.
" Quite a lot is known about the group of diffeomorphisms of the circle. Its Lie algebra ...
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