Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with differential-topology
Search options not deleted
user 450
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”.
18
votes
Smooth homotopy theory
Dear Paul, as Ryan says the smooth and continuous homotopy groups of a manifold coincide.
This is stated as Corollary 17.8.1 in Bott and Tu's book Differential Forms in Algebraic Topology (Springer G …
- 47.5k
39
votes
lefschetz hyperplane section theorem
Dear anonymous, let $ X \subset \mathbb P^n(\mathbb C)$ be a smooth hypersurface of degree $d$ in projective space. Let me show how Lefschetz directly calculates the homology $H_i(X)=H_i(X,\mathbb Z) …
- 47.5k
4
votes
Can one glue De Rham cohomology classes on a differential manifolds?
Here is the solution obtained by one of my brilliant geometer friends evoked in the question:
Take $X=S^2$, the unit $2$-sphere with equation $x_1^2+x_2 ^2+x_3^2=1$, and cover it by the three open str …
- 47.5k
4
votes
Can one glue De Rham cohomology classes on a differential manifolds?
Here is the great answer given by another of my brilliant friends:
Let $X$ be $\mathbb C, U_0$ be the open complement in $X$ of the closed disk $\bar D=\{z\in \mathbb C\vert \vert z\vert \leq1 \}$
and …
- 47.5k
17
votes
4
answers
1k
views
Can one glue De Rham cohomology classes on a differential manifolds?
Let $M$ be a differential manifold and $\mathcal H^k$ the presheaf of real vector spaces associating to the open subset $U\subset M$ the $k$-th de Rham cohomology vector space: $\mathcal H^k(U)=H^k_{D …
- 47.5k
5
votes
1
answer
196
views
Finding a volume form on a fibre of a submersion between oriented manifolds
Let $f:X\to Y$ be a submersion between orientable smooth manifolds of respective dimensions $n,p$ and let $j:M=f^{-1}(y)\hookrightarrow X$ denote the inclusion of some fibre of $f$.
My naïve (I am no …
- 47.5k
19
votes
0
answers
312
views
Can one properly embed a differential manifold into numerical space of double dimension? [duplicate]
If $X$ is a $ C^\infty$ differential manifold of dimension $n$, then there exists an embedding $f:X\to \mathbb R^{2n+1}$.
This is a not too difficult theorem due to Whitney, proved in many textbooks. …
- 47.5k