  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).
