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Homotopy theory, homological algebra, algebraic treatments of manifolds.

5 votes

Visualizing how Cech cohomology detects holes

This is explained in "Principles of Algebraic Geometry," by Griffiths & Harris, p42. Given a simplicial decomposition of your space, associate each vertex $v_\alpha$ with its star $U_\alpha$, where th …
Martin Sleziak's user avatar
6 votes

What (if anything) happened to Intersection Homology?

There do seem to be people thinking about it. I heard Sylvain Cappell lecture a few weeks ago; he spoke about using intersection (co)homology as part of a generalization of characteristic classes to s …
Martin Sleziak's user avatar