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Results tagged with smooth-manifolds
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user 1306
Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
10
votes
$A_{\infty}$-structure on closed manifold
If you require just "not homeomeorphic", then there are very silly examples of all sorts. What you want to ask is "not homotopic", I suppose.
For that, I know some useful references in "Which H-spac …
- 16.9k
2
votes
Accepted
Does an analytic tensorial Lie structure on $S^2$ gives a fiberwise Abelian Lie algebra stru...
No. A skew-symmetric bilinear map $V\times V\to V$ satisfies the Jacobi identity automatically if $\dim V=2$ since the Jacobi identity is skew-symmetric in its arguments. So if you take a generic skew …
- 16.9k
4
votes
Configuration spaces of the torus
I would suggest the two following references:
C.-F. Bödigheimer, F.R. Cohen, Rational cohomology of configuration spaces of surfaces. Algebraic Topology and Transformation Groups, Springer LNM 1361 ( …
- 16.9k
15
votes
Accepted
definition of Hessian with respect to connection
(This is an elaboration on the comment of MG. I know I benefited a lot as an undergraduate from being shown this sort of argument once instead of having been told to check things in local coordinates, …
- 16.9k