2019/07/16 by Cheuk Yu Mak, Ivan Smith, Mak, Cheuk Yu +1
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.1907.07624
We realise Stroppel's extended arc algebra in the Fukaya-Seidel category of a\nnatural Lefschetz fibration on the generic fiber of the adjoint quotient map on\na type A nilpotent slice with two Jordan blocks, and hence obtain a\nsymplectic interpretation of certain parabolic two-block versions of\nBernstein-Gelfan'd-Gelfan'd category \O. As an application, we give\na new geometric construction of the spectral sequence from annular to ordinary\nKhovanov homology. The heart of the paper is the development of a cylindrical\nmodel to compute Fukaya categories of (affine open subsets of) Hilbert schemes\nof quasi-projective surfaces, which may be of independent interest.\n