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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
45
votes
6
answers
6k
views
Universal definition of tangent spaces (for schemes and manifolds)
Both schemes and manifolds are local ringed spaces which are locally isomorphic to spaces in some full subcategory of local ringed spaces (local models). Now, there is the inherent notion of the Zaris …
2
votes
How much of differential geometry can be developed entirely without atlases?
There is something called abstract differential geometry "developed" by Mallios et al (wikipedia). Perhaps you should skim through the first chapter of his book "Modern Differential Geometry in Gauge …
2
votes
Dolbeault cohomology
If I remember right there should be something in "Differential Analysis on Complex Manifolds" by Wells.