Cohomology rings of real flag manifolds

Speaker(s)

Akos Matszangosz

Affiliation

Renyi Institute (Budapeszt)

Date

April 20, 2021, 4:30 p.m.

Information about the event

Zoom: 892 1108 9551 Password - type the number equal to rk(H^2((S^1)^{200};Z))

Seminar

Seminar Algebraic Topology

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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.

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