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2d
comment Connection in fibre bundle from discontinuous group action
@Bombyxmori I think it is reasonable, considering that I "act in every direction". The formal argument I know invokes Poincaré duality to conclude: if a group $\Gamma$ acts (faithfully) on a contractible manifold $X$ and $\mathrm{cd} \, \Gamma = \dim X$, then $X / \Gamma$ is compact. ($\mathrm{cd}$ being the "cohomological dimension".)
2d
revised Connection in fibre bundle from discontinuous group action
deleted 89 characters in body
Jul
2
awarded  Curious
Jun
22
awarded  Nice Question
Jun
17
awarded  Yearling
Jun
12
comment Number of Zeros of a Section vs Integral First Chern Class
Thanks. Any hint as to why this is true?
Jun
12
comment Number of Zeros of a Section vs Integral First Chern Class
"complex line bundles are actually classified by their first Chern class" Is this true for bundles over any base space?
May
18
reviewed Reviewed Solving of the first-order nonlinear differential equation
May
17
reviewed Reviewed Lie group, differential of multiplication map
May
17
reviewed No Action Needed Given three continuous and diffrentiable functions satisfying given condition, which of the following options are correct
Mar
19
comment Can one exchange fibre and base space in a fibre bundle?
@geodude My question was about "general fibre bundles", I'm not really interested in direct products. Thank you for the link.
Mar
18
accepted Sheaf cohomology of projective spaces
Feb
9
awarded  Critic
Jan
27
asked Can one exchange fibre and base space in a fibre bundle?
Jan
23
awarded  Tumbleweed
Jan
23
revised Connection in fibre bundle from discontinuous group action
added 37 characters in body
Jan
23
comment All almost complex structures on a manifold
@JimBelk $\mathcal O(k)$ is the complex line bundle (real rank 2 bundle) of Chern class $k$ over $\mathbb P^1\cong S^2$ (see the notation on Wikipedia). I loosely expect the space to be finite-dimensional, because the space of complex structures on $\mathcal O(k)$, $k$ neg., is finite-dimensional (this one has to calculate). Even if it isn't finite-dimensional, though, one should be able to construct at least a one-parameter family of almost complex structures for the theorem to be of any practical value.
Jan
22
reviewed Reviewed How is statistical uncertainty calculated for the modulus function?
Jan
22
reviewed Reviewed How do I prove this statement is tautology without using truth tables?
Jan
22
reviewed Reviewed How to derive the Descartes equation of a line in a coordinate system? $ax+by+c=0$