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Results tagged with differential-topology
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user 10333
The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
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Contractible noncompact 3-manifold without boundary not homeomorphic to $\Bbb R^3$
I heard this example was given in Whitehead's paper A CERTAIN OPEN MANIFOLD WHOSE GROUP IS UNITY.( http://qjmath.oxfordjournals.org/content/os-6/1/268.full.pdf ) But I was confused by his term. Thus I …
- 1,079
8
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4
answers
924
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How does all of the bundles over a certain manifold characterize the homotopy class of the b...
It is known that if $f:M\rightarrow N$ is a homotopy equivalent, then the the process of pullback gives a one-one correspondence between bundles over $N$ and $M$ up to isomorphism. Is the converse( th …
- 1,079
8
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602
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Can a smooth, immersed loop in R^2 become not nullhomotopic by removing a point?
ATT
More precisely, let $\gamma :S^1\rightarrow R^2$ be a smooth immersed loop, the question is whether it is true that there is a point $p\in R^2-\gamma(S^1)$ such that $\gamma$ is not homotopic to …
- 1,079