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Results tagged with dg.differential-geometry
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user 126667
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
20
votes
Least number of charts to describe a given manifold
To answer your last question, the least number of charts needed to cover any orientable 2-manifold is 2. Consider the usual embedding of an orientable surface Σ in R3 which is symmetric across the pl …
- 25.2k
18
votes
Is it possible to capture a sphere in a knot?
The regular dodecahedron is not a local minimum for total edge length either. Consider the five vertices Vi, i = 1, ..., 5 of a face together with the "center" C of the face. The spherical triangle …
- 25.2k
9
votes
Important results that use infinite-dimensional manifolds?
Infinite-dimensional Grassmannians and their tautological bundles arise in topological K-theory and bordism. See Thom's Quelques propriétés globales des variétés differentiables.