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PreprintarXiv licencearXiv

Every Link Has Infinitely Many Explicit Generalised T-Link Presentations

  • Thiago de Paiva
  • Yi Liu
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Abstract

Generalised T-links provide a simple description of all links in S3 as closures of products of standard twisting blocks, parametrised by finite sequences of integers. We prove that every link admits infinitely many pairwise distinct generalised T-link presentations. Starting from any such presentation, we give explicit parameter transformations that preserve the represented link and generate families of pairwise distinct presentations depending on arbitrarily many independent integer parameters.

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Cite

BibTeXRIS
BibTeX
@misc{paiva2026every,
  title = {{Every Link Has Infinitely Many Explicit Generalised T-Link Presentations}},
  author = {Thiago de Paiva and Yi Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25683},
  eprint = {2609.25683},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25683},
}
RIS
TY  - UNPB
TI  - Every Link Has Infinitely Many Explicit Generalised T-Link Presentations
AU  - Thiago de Paiva
AU  - Yi Liu
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25683
UR  - https://arxiv.org/abs/2609.25683
AB  - Generalised T-links provide a simple description of all links in S^3 as closures of products of standard twisting blocks, parametrised by finite sequences of integers. We prove that every link admits infinitely many pairwise distinct generalised T-link presentations. Starting from any such presentation, we give explicit parameter transformations that preserve the represented link and generate families of pairwise distinct presentations depending on arbitrarily many independent integer parameters.
ER  -