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Homotopy theory, homological algebra, algebraic treatments of manifolds.

11 votes

Any shortcuts to understanding the properties of the Riemannian manifolds which are used in ...

There's a short book by Milnor: "Topology from a differentiable viewpoint" (here is one link https://math.uchicago.edu/~may/REU2017/MilnorDiff.pdf where you can find it).
David Lehavi's user avatar
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2 votes

How to demonstrate $SO(3)$ is not simply connected?

You have two different proofs (a.k.a. the cup proof and the belt proof) right here http://www.youtube.com/watch?v=CYBqIRM8GiY There are several different demonstrations of the second one (Harrison …
David Lehavi's user avatar
  • 4,394
9 votes

Computing fundamental groups and singular cohomology of projective varieties

The trick I know (learned it from Ron Livne) is to project it to some space with known homotopy / homology, throw away the ramification and branch loci to get a covering map (and you better pray it's …
David Lehavi's user avatar
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9 votes

Etale cohomology -- Why study it?

One of the annoying aspects with sheaf cohomology in algebraic geometry is that - even for curves over the complex numbers - the cohomological dimensions are not what you want them to be, if you are u …
David Lehavi's user avatar
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