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PreprintarXiv licencearXiv

Derivative links in contact topology

  • Joseph Breen
  • Alexander Zupan
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Abstract

We import the theory of R-links and derivative links into contact topology in both the Legendrian and transverse setting. This framework is used to characterize various forms of Lagrangian and symplectic sliceness, and more generally establishes one approach to what we call the Lagrangian slice-ribbon conjecture. Our main theorem asserts that a Legendrian knot with Thurston-Bennequin invariant −1 is Lagrangrian slice (resp. regularly Lagrangian slice) if and only if it supports a tight transverse (resp. Legendrian) R-link derivative.

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Cite

BibTeXRIS
BibTeX
@misc{breen2026derivative,
  title = {{Derivative links in contact topology}},
  author = {Joseph Breen and Alexander Zupan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30182},
  eprint = {2609.30182},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30182},
}
RIS
TY  - UNPB
TI  - Derivative links in contact topology
AU  - Joseph Breen
AU  - Alexander Zupan
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30182
UR  - https://arxiv.org/abs/2609.30182
AB  - We import the theory of R-links and derivative links into contact topology in both the Legendrian and transverse setting. This framework is used to characterize various forms of Lagrangian and symplectic sliceness, and more generally establishes one approach to what we call the Lagrangian slice-ribbon conjecture. Our main theorem asserts that a Legendrian knot with Thurston-Bennequin invariant −1 is Lagrangrian slice (resp. regularly Lagrangian slice) if and only if it supports a tight transverse (resp. Legendrian) R-link derivative.
ER  -