The Fukaya $A_\infty$ algebra of a non-orientable Lagrangian

Autor:	Kedar, Or, Solomon, Jake P.
Rok vydání:	2022
Předmět:	Mathematics - Symplectic Geometry High Energy Physics - Theory Mathematics - Algebraic Geometry 53D37 53D40 (Primary) 55N25 53D12 58J32 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Let $L\subset X$ be a not necessarily orientable relatively $Pin$ Lagrangian submanifold in a symplectic manifold $X$. We construct a family of cyclic unital curved $A_\infty$ structures on differential forms on $L$ with values in the local system of graded non-commutative rings given by the tensor algebra of the orientation local system of $L$. The family of $A_\infty$ structures is parameterized by the cohomology of $X$ relative to $L$ and satisfies properties analogous to the axioms of Gromov-Witten theory. On account of the non-orientability of $L,$ the evaluation maps of moduli spaces of $J$-holomorphic disks with boundary in $L$ may not be relatively orientable. To deal with this problem, we use recent results on orientor calculus. Comment: 58 pages, includes summary of relevant background from arXiv:2211.05117
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.05439 Zobrazit plný text záznamu View this record from Arxiv