Density of fibers for the filtered Fukaya category of $T^*N$

TL;DR

This paper proves that in the Fukaya category of a cotangent bundle, the iterated cones of fibers over a dense set of basepoints are dense, confirming a conjecture by Biran and Cornea.

Contribution

It establishes the density of iterated cones of cotangent fibers in the filtered Fukaya category, answering a key question in symplectic geometry.

Findings

Iterated cones of fibers form a dense subset in the Fukaya category.

Confirms a conjecture by Biran and Cornea.

Advances understanding of the structure of the Fukaya category.

Abstract

We answer a question of Biran and Cornea about the density of iterated cones of fibers in the Fukaya category of a cotangent bundle. We prove that indeed if we take a dense set of basepoints, the iterated cones of the cotangent fibres are dense in the Filtered Fukaya category.