Year: 2025
Type: preprint
Abstract: In previous work, we introduced a version of the Fukaya algebra associated to a degeneration of a symplectic manifold, whose structure maps count collections of maps in the components of the degeneration satisfying matching conditions. In this paper, we introduce a further degeneration of the matching conditions (similar in spirit to Bourgeois' version of symplectic field theory) which results in a "split Fukaya algebra" whose structure maps are, in good cases, sums of products over vertices of tropical graphs. In the case of toric Lagrangians contained in a toric component of the degeneration, an invariance argument implies the existence of projective Maurer-Cartan solutions, which gives an alternate proof of the unobstructedness result of Fukaya-Oh-Ohta-Ono for toric manifolds. Our result also proves unobstructedness in more general cases, such as for toric Lagrangians in almost toric four-manifolds.
Source: arXiv (Cornell University)
Authors: Venugopalan, Sushmita, Woodward, Chris
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6910699080
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