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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
4
votes
A comprehensive functor of points approach for manifolds
I certainly wouldn't call it an "attack with abstract nonsense", but the "functor of points" language can also be used in the context of differentiable manifolds. A very good place to start would be …
6
votes
Harmonic Expansion
I'd look in books on representation theory rather than books on homogeneous vector bundles for this sort of thing. Perhaps George Mackey's famous book "Unitary group representations in physics, proba …
11
votes
Stokes theorem for manifolds with corners?
If you are looking for an online reference, you can check out Brian Conrads course notes on differential geometry. Near the bottom of that page, you can find the handout with Stokes theorem for manif …
7
votes
Accepted
When is a homogeneous space a variety?
I'll try to answer both questions, though I will change the first question somewhat. Let's work in the setting of a real reductive algebraic group $G$ and a closed subgroup $H \subset G$.
Your fir …
1
vote
Does $\mathrm{E}_7/(\mathrm{SU}_8/(\mathbb{Z}/2))$ carry an almost complex structure?
The following is mostly bogus, based on my overly quick reading and misunderstanding of the question:
No. $E_7 / (SU(8)/\mu_2)$ (where $E_7$ here denotes the compact real Lie group) is not a Hermiti …
23
votes
1
answer
2k
views
Do hyperKahler manifolds live in quaternionic-Kahler families?
A geometry question that I thought about more seriously a few years ago... thought it'd be a good first question for MO.
I'm aware that there are a number of Torelli type theorems now proven for comp …
12
votes
Historical use of figures in geometry
Maybe this isn't an answer, but below is a photograph of the tablet BM15285 (British Museum catalog #15285). It's a series of geometry problems, from c.1800 BCE (+/- 200 years?). There are plenty mo …