On the Topology of Spaces of Smooth Sections of Homogeneous Vector Bundles

Student: Konovalov Nikolai

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2016

In this paper we study the topology of the space $\Gamma(X,L)_{reg}$. This space is the topological space of smooth sections of the $G$-equivariant line bundle $L$ over the generalized complete flag variety $X:=G/B$. We define natural cohomological classes $\Lk^{\Sing}_w\in H^*(\Gamma(X,L)_{reg})$ and compute the action on these classes of the orbit map $O\colon G\to\Gamma(X,L)_{reg}$.

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