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On the Upsilon invariant and the Baldwin-Vela-Vick b-invariant of fibered knots

  • Linh Truong
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Abstract

For a null-homologous fibered knot K in a rational homology sphere, Baldwin and Vela-Vick define a refinement b(K) of the Ozsváth-Szabó contact invariant. We prove that if the Ozsváth-Stipsicz-Szabó concordance invariant Upsilon has slope Υ'K(t)=−g(K) for some t∈[0,2/(n+1)), where g(K) is the genus of K, then b(K)>n. This extends a result of He, Hubbard, and the author on the Upsilon invariant and right-veering monodromies. We also prove that the knot Floer homology of a fibered knot in the $g(K)-b(K)$ Alexander grading is nonvanishing. As an application, we give many families of fibered cable knots whose b(K) invariant grows arbitrarily large. Finally, we prove that if a monodromy of a fibered knot is neither right-veering nor left-veering, then the third-to-top term of knot Floer homology is nonvanishing.

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Cite

BibTeXRIS
BibTeX
@misc{truong2026upsilon,
  title = {{On the Upsilon invariant and the Baldwin-Vela-Vick b-invariant of fibered knots}},
  author = {Linh Truong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33280},
  eprint = {2610.33280},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33280},
}
RIS
TY  - UNPB
TI  - On the Upsilon invariant and the Baldwin-Vela-Vick b-invariant of fibered knots
AU  - Linh Truong
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33280
UR  - https://arxiv.org/abs/2610.33280
AB  - For a null-homologous fibered knot K in a rational homology sphere, Baldwin and Vela-Vick define a refinement b(K) of the Ozsváth-Szabó contact invariant. We prove that if the Ozsváth-Stipsicz-Szabó concordance invariant Upsilon has slope Υ'_K(t)=−g(K) for some t∈[0,2/(n+1)), where g(K) is the genus of K, then b(K)>n. This extends a result of He, Hubbard, and the author on the Upsilon invariant and right-veering monodromies. We also prove that the knot Floer homology of a fibered knot in the $g(K)-b(K)$ Alexander grading is nonvanishing. As an application, we give many families of fibered cable knots whose b(K) invariant grows arbitrarily large. Finally, we prove that if a monodromy of a fibered knot is neither right-veering nor left-veering, then the third-to-top term of knot Floer homology is nonvanishing.
ER  -