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Results tagged with dg.differential-geometry
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user 21095
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
40
votes
Converse of Poincaré-Hopf theorem
$\newcommand{\ZZ}{\mathbb{Z}}$$\newcommand{\CC}{\mathbb{C}}$A simple counter-example is given by $M = \CC P^3$.
Recall first that the cohomology ring of $\CC P^3$ is a truncated polynomial algebra:
$ …
- 6,210
34
votes
1
answer
4k
views
Strong Whitney embedding theorem for non-compact manifolds
$\newcommand{\RR}{\mathbb{R}}$The present question arises from some confusion on my part regarding the precise statement of the strong Whitney embedding theorem for non-compact manifolds.
The strong …
- 6,210
9
votes
Accepted
C^2 submanifolds contained in a hypersurface
The answer is negative.$\newcommand{\RR}{\mathbb{R}}$$\newcommand{\abs}[1]{\lvert #1 \rvert}$$\newcommand{\set}[1]{\left\lbrace #1 \right\rbrace}$$\newcommand{\ceiling}[1]{\left\lceil #1 \right\rceil} …
- 6,210
4
votes
From Topological to Smooth and Holomorphic Vector Bundles
I am under the impression that some of the answers given may be interpreting question (A) in a manner which does not seem --- at least to me --- entirely consistent with how it is stated. Interpreting …
- 6,210
4
votes
Homotopy Equivalences and Induced Correspondences between Fibre Bundles
Here is a quick argument which proves homotopy equivalence directly. First, the pullback of a homotopy equivalence along a Hurewicz fibration is again a homotopy equivalence. Further, by the well-know …
- 6,210