arXiv Open Access 2022

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

Or Kedar Jake P. Solomon

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.SG hep-th math.AG

Penulis (2)

Or Kedar

Jake P. Solomon

Format Sitasi

APA MLA BibTeX

Kedar, O., Solomon, J.P. (2022). The Fukaya $A_\infty$ algebra of a non-orientable Lagrangian. https://arxiv.org/abs/2211.05439

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓