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Sem. Topologia Alg.

 

Cohomology rings of real flag manifolds


Prelegent: Akos Matszangosz

2021-04-20 16:30

The cohomology ring of a complex (partial) flag manifold has two classical descriptions; a topological one (via characteristic classes) and a geometric one (via Schubert classes). Similar descriptions are well-known for real flag manifolds X with mod 2 coefficients. In this talk I will discuss some aspects of what can be said with rational, or integer coefficients. Namely, I will consider questions of the following type:

1) Which Schubert varieties represent an integer cohomology class?
2) What are their structure constants?
3) What can be said about torsion in H^*(X;\Z)?

I will also discuss some applications of the ring structure to real Schubert calculus.