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Results tagged with dg.differential-geometry
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user 2039
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
18
votes
de Rham cohomology and flat vector bundles
A flat connection on a vector bundle of dimension determines a local system $\mathcal{G}$ over your base manifold $M$ by parallel transport, i. e. a functor from the fundamental groupoid of $M$ to the …
- 12.1k
12
votes
Conceptual proof of classification of surfaces?
This is more an extended comment than an answer to the question. The first thing to note is that there are different strenghts of the classification theorem for surfaces. Of course, there are the diff …
- 12.1k
5
votes
A list of machineries for computing cohomology
1) If you want to compute the rational or real cohomology of something, you can try to use rational homotopy theory. Rational homotopy theory says that the rational singular chain complex is (as a dga …