From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron
arXiv:2009.03981 · doi:10.1007/s00029-024-00932-8
Abstract
We give a conjectural algebraic description of the Fukaya category of a complexified hyperplane complement, using the algebras defined in arXiv:0905.1335 from the equivariant cohomology of toric varieties. We prove this conjecture for cyclic arrangements by showing that these algebras are isomorphic to algebras appearing in work of Ozsvath-Szabo arXiv:1603.06559 in bordered Heegaard Floer homology arXiv:0810.0687. The proof of our conjecture in the cyclic case extends work of Karp-Williams arXiv:1608.08288 on sign variation and the combinatorics of the m=1 amplituhedron. We then use the algebras associated to cyclic arrangements to construct categorical actions of gl(1|1).
42 pages, eps figures
References in corpus (7)
- Total positivity, Grassmannians, and networks
- Affine highest weight categories and affine quasihereditary algebras
- A categorification of U_q sl(1,1) as an algebra
- Hyperkahler analogues of Kahler quotients
- Algebras with matchings and knot Floer homology
- Ozsvath-Szabo bordered algebras and subquotients of category O
- Generators, relations, and homology for Ozsváth-Szabó's Kauffman-states algebras