From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron

Aaron D. Lauda; Anthony M. Licata; Andrew Manion

doi:10.1007/s00029-024-00932-8

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arXiv · 2009.03981

From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron

Aaron D. Lauda·Anthony M. Licata·Andrew Manion

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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).

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Aaron D. Lauda, Anthony M. Licata, Andrew Manion. 2020-09-08. From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron. https://doi.org/10.1007/s00029-024-00932-8

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