Bordered Floer Theory Unifies Lagrangian and Knot Homology via Torus Categories — E8 Intelligence Research

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Lagrangian Floer homology and knot Floer homology are unified through bordered Floer theory, revealing a categorical correspondence between symplectic geometry and low-dimensional topology. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22720181

September 12, 2026Open Access

Bordered Floer Theory Unifies Lagrangian and Knot Homology via Torus Categories — E8 Intelligence Research

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Key Points

To establish a unifying categorical correspondence between Lagrangian Floer homology in symplectic geometry and knot Floer homology in 3-manifold topology using bordered Floer theory.
Analyzed categorical operations in the Fukaya category of the 2-torus alongside Ext groups for Lagrangian submanifolds.
Formulated bordered Floer homology modules over torus algebras arising from Lagrangian torus fibrations with affine structures.
Identified a direct algebraic correspondence between Fukaya categories of tori and low-dimensional knot Floer invariants.
Linked the affine geometry of the torus fibration to the A1 × A1 root lattice and modular group actions.
Connected knot cohomology rank bounds qualitatively to hyperbolic volume through a conjectured positive real scaling constant.

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Implication

Theoretical analysis demonstrates unification of Lagrangian and knot Floer homology in torus categories, indicating a bridge between symplectic geometry and 3-manifold topology.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7b3df0926e14a848b3311 https://doi.org/10.5281/zenodo.22720181

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Bordered Floer Theory Unifies Lagrangian and Knot Homology via Torus Categories — E8 Intelligence Research

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Bordered Floer Theory Unifies Lagrangian and Knot Homology via Torus Categories — E8 Intelligence Research

Key Points

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Implication

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