Algebra Commons^™

Equivariant Intersection Cohomology Of Bxb Orbit Closures In The Wonderful Compactification Of A Group, Stephen Oloo

Doctoral Dissertations

This thesis studies the topology of a particularly nice compactification that exists for semisimple adjoint algebraic groups: the wonderful compactification. The compactifica- tion is equivariant, extending the left and right action of the group on itself, and we focus on the local and global topology of the closures of Borel orbits. It is natural to study the topology of these orbit closures since the study of the topology of Borel orbit closures in the flag variety (that is, Schubert varieties) has proved to be inter- esting, linking geometry and representation theory since the local intersection cohomology Betti numbers turned out …