English

A TQFT-based Platform for Efficient Computation of Knot Invariants

Geometric Topology 2026-07-26 v1 Mathematical Software High Energy Physics - Theory Mathematical Physics Quantum Physics

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.

Cite

@article{arxiv.2607.23551,
  title  = {A TQFT-based Platform for Efficient Computation of Knot Invariants},
  author = {Amena Al Rawi and Hisham Sati and Vivek Kumar Singh},
  journal= {arXiv preprint arXiv:2607.23551},
  year   = {2026}
}

Comments

20 pages, 8 figures, Software available at: https://tqft-knot-explorer-559830223866.me-central1.run.app/