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Results tagged with dg.differential-geometry
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user 85592
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
8
votes
Hodge map and the Cohomology Ring of a Riemannian Manifold
As has been observed in the comments, it suffices to construct a closed differential form $\omega$ for which $\star\omega$ is not closed. Here is an explicit example.
Let $M$ be the circle $S^1$ for …
- 1,424
8
votes
Accepted
Regarding the surgery construction in "A procedure for killing homotopy groups of differenti...
There is no error in the paper as far as I can tell. One thinks of the surgery as taking out the interior of the image of $S^p\times D^{q+1}$, and glueing in a copy of $D^{p+1}\times S^q$ along the co …
- 1,424
6
votes
Conceptual proof of classification of surfaces?
Using a little bit of real algebraic geometry, there is a conceptual proof at least in the critical case $\chi=-1$, i.e. the case you're talking about explicitly. Indeed, let $S$ be a compact connecte …
- 1,424
3
votes
Accepted
Does complexified isometry group act transitively on tangent bundle of compact Riemannian ma...
Maybe these arguments are of interest to you. It is known that for any compact symmetric space $M$ the tangent bundle $TM$ possesses a canonical structure of a complex
manifold. Multiplication by $-1$ …
- 1,424