A TQFT-based Platform for Efficient Computation of Knot Invariants

Amena Al Rawi; Hisham Sati; Vivek Kumar Singh

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arXiv · 2607.23551

A TQFT-based Platform for Efficient Computation of Knot Invariants

Amena Al Rawi·Hisham Sati·Vivek Kumar Singh

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Abstract

We present an interactive web platform that unifies the construction Feynman ribbon diagrams (FRDs), the evaluation of higher-rank Chern--Simons knot invariants, and the identification of FRD-like knots at higher crossing numbers. These tree-structured diagrams naturally represent arborescent knots, which we refer to throughout as FRD-like knots. Within a single visual environment, users can construct an FRD as a tensor network, evaluate its associated Chern--Simons invariants, and use the resulting invariant data to distinguish and identify the corresponding knot. To our knowledge, this is the first platform to combine diagrammatic construction, tensor-network evaluation, invariant computation, and knot identification within a unified workflow.

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Amena Al Rawi, Hisham Sati, Vivek Kumar Singh. 2026-07-26. A TQFT-based Platform for Efficient Computation of Knot Invariants. https://arxiv.org/abs/2607.23551

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