Fukaya category with curves of higher genus
M. V. Movshev
TL;DR
This paper introduces a new formalism for defining Fukaya categories that incorporate higher genus curves, expanding the mathematical framework for symplectic geometry and mirror symmetry.
Contribution
It presents a novel approach to include higher genus curves in the Fukaya category, which was previously limited to lower genus cases.
Findings
Developed a formalism for higher genus curves in Fukaya categories
Extended the applicability of Fukaya categories to more complex geometries
Lays groundwork for future research in symplectic topology and mirror symmetry
Abstract
We introduce a formalism which allows us to formulate a version of Fukaya category in presence of curves of higher genus.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory