Work

Non-archimedean analytic continuation of unobstructedness

Year: 2025

Type: article

Abstract: The Floer cohomology and the Fukaya category are not defined in general. Indeed, while the issue of obstructions can be theoretically addressed by introducing bounding cochains, the actual existence of even one such bounding cochain is usually unknown. This paper aims to deal with the problem. We study a certain non-archimedean analytic structure that enriches the Maurer–Cartan theory of bounding cochains. Using this rigid structure and family Floer techniques, we prove that, within a connected family of graded Lagrangian submanifolds, if any one Lagrangian is unobstructed (in a slightly stronger sense), then all remaining Lagrangians are automatically unobstructed.

Source: Quantum Topology

DOI: 10.4171/qt/237

Author: Hang Yuan

Institution: Beijing Institute of Mathematical Sciences and Applications

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4410776342

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