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Homotopy theory, homological algebra, algebraic treatments of manifolds.

2 votes

What is the "right" definition of the homology(cohomology) of an orbifold?

I do not know the current state of the art, but I can point you to the paper of Chen and Ruan which should have everything you are asking for.
Michael Joyce's user avatar
6 votes

Cohomology ring of a flag variety and representation theory

Both the study of ordinary Schubert calculus (the ordinary, e.g. Borel-Moore, cohomology of Schubert varieties of the flag variety) and the study of Kazhdan-Lusztig theory (the intersection cohomology …
Michael Joyce's user avatar
3 votes

Reading list for Equivariant Cohomology

Some additional resources, which are more on the algebraic side than the symplectic side: 1) Bill Fulton's Eilenberg lectures on Equivariant Cohomology in Algebraic Geometry, available at David Ander …
Michael Joyce's user avatar