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PreprintCC BY 4.0arXiv

Unknotting number and L-space satellite operations

  • Daren Chen
  • Ian Zemke
  • Hugo Zhou
Open at sourcePDFDOICite

Abstract

We give a lower bound for the unknotting number under the L-space satellite operations. In the case of braided L-space satellite operations, including cabling operations, we obtain a stronger bound. The proof uses a lower bound for the unknotting number in knot Floer homology due to Alishahi-Eftekhary. The computational tool is a formula for computing the knot Floer complex under the L-space satellite operations, which was defined in the authors' previous work.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026unknotting,
  title = {{Unknotting number and L-space satellite operations}},
  author = {Daren Chen and Ian Zemke and Hugo Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14520},
  eprint = {2609.14520},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14520},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Unknotting number and L-space satellite operations
AU  - Daren Chen
AU  - Ian Zemke
AU  - Hugo Zhou
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14520
UR  - https://arxiv.org/abs/2609.14520
AB  - We give a lower bound for the unknotting number under the L-space satellite operations. In the case of braided L-space satellite operations, including cabling operations, we obtain a stronger bound. The proof uses a lower bound for the unknotting number in knot Floer homology due to Alishahi-Eftekhary. The computational tool is a formula for computing the knot Floer complex under the L-space satellite operations, which was defined in the authors' previous work.
ER  -