L-Space Knots in sl_n-like Knot Floer Homology

@misc{wells2026lspace,
  title = {{$L$-Space Knots in $\mathfraksl_n$-like Knot Floer Homology}},
  author = {Tristan Wells},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38927},
  eprint = {2610.38927},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38927},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - L-Space Knots in sl_n-like Knot Floer Homology
AU  - Tristan Wells
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38927
UR  - https://arxiv.org/abs/2610.38927
AB  - It has been of particular interest in recent years to relate categorifications of quantum knot invariants like the Jones polynomial to Floer-theoretic invariants like knot Floer homology using spectral sequences. In pursuit of Rasmussen's conjecture, Dowlin constructed a family of invariants with properties like those of Khovanov and Rozansky's sl_n-homology theories. In this paper, we explore these invariants for L-space knots and thin knots. In particular, for n≥ 2 the invariants of thin knots can be computed from a change of coefficients from the minus flavor of knot Floer homology, and the same holds for an L-space knot exactly when an explicit condition relating n to its Alexander polynomial is satisfied.
ER  -