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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

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 …
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2 votes

Dolbeault cohomology

If I remember right there should be something in "Differential Analysis on Complex Manifolds" by Wells.
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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 …
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