Bordered Floer Homology Bridges Knot Invariants and Torus Fukaya Categories — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-19
DOI
https://doi.org/10.5281/zenodo.22841457
Primary Topic
Geometric and Algebraic Topology
Type
preprint
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preprint

Bordered Floer Homology Bridges Knot Invariants and Torus Fukaya Categories — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Geometric and Algebraic Topology
preprint

Bordered Floer Homology Bridges Knot Invariants and Torus Fukaya Categories — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Bordered Floer homology provides a categorical framework linking knot Floer homology to the Fukaya category of the torus, with new conjectures connecting hyperbolic volume to knot cohomology growth rates. MATH: - **Bordered Floer homology**: A functor from pointed 3-manifolds with torus boundary to a category of modules over a differential graded algebra (the "torus algebra" \(\mathcal{A}(\mathbb{T}^2)\)). - **Fukaya category of the torus**: \(\mathcal{F}uk(\mathbb{T}^2)\) — objects are Lagrangian submanifolds (e.g., simple closed curves with slopes \(p/q \in \mathbb{Q} \cup \{\infty\}\)), morphisms are Floer cohomology \(HF^*(L_1, L_2)\), with \(A_\infty\)-structure. - **Atiyah–Floer conjecture**: Relates instanton Floer homology of a 3-manifold to Lagrangian intersection Floer homology in a moduli space of flat connections (gauge-theoretic vs. symplectic). - **New conjectures (arXiv:2307.03297)**: For knots with crossing number \(c\), there exists \(a > 0\) such th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Geometric and Algebraic Topology
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Bordered Floer Homology Bridges Knot Invariants and Torus Fukaya Categories — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS