Exotic Springer fibers for orbits corresponding to one-row bipartitions

Abstract

We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the structure of the irreducible components and their intersections as well as the construction of an explicit affine paving. Moreover, we compute the ring structure of cohomology by constructing a CW-complex homotopy equivalent to the exotic Springer fiber. This homotopy equivalent space admits an action of the type C Weyl group inducing Kato's original exotic Springer representation on cohomology. Our results are described in terms of the diagrammatics of the two-boundary Temperley-Lieb algebra. This provides a first step in generalizing the geometric versions of Khovanov's arc algebra to the exotic setting.

HOMFLYPT homology for links in handlebodies via type A Soergel bimodules

“…One fertile avenue is the possible connection between the g 1 case and versions of Springer fibers as e.g. in [Ka09] or [SW18].…”