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A Concordance Invariant For Knots from CFK∞

  • Kashti Satish Umare
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Abstract

We construct a multi-filtered smooth knot concordance invariant, β(t1, a, t2), derived from the knot Floer complex CFK∞. β is a three-variable piecewise linear function defined on (0,2) × ℝ × (0,2). We demonstrate that β satisfies a subadditivity relation. We apply β to prove concordance results for a certain family of L-space knots. We show that the positive cones spanned by Teragaito's knots K1,n and K2,n are disjoint in the smooth concordance group 𝒞. For positive L-space knots, we show β completely determines the Alexander polynomial and distinguishes knots with identical Υ invariants.

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Cite

BibTeXRIS
BibTeX
@misc{umare2026concordance,
  title = {{A Concordance Invariant For Knots from $CFK^\infty$}},
  author = {Kashti Satish Umare},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30425},
  eprint = {2609.30425},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30425},
}
RIS
TY  - UNPB
TI  - A Concordance Invariant For Knots from CFK^∞
AU  - Kashti Satish Umare
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30425
UR  - https://arxiv.org/abs/2609.30425
AB  - We construct a multi-filtered smooth knot concordance invariant, β(t^1, a, t^2), derived from the knot Floer complex CFK^∞. β is a three-variable piecewise linear function defined on (0,2) × ℝ × (0,2). We demonstrate that β satisfies a subadditivity relation. We apply β to prove concordance results for a certain family of L-space knots. We show that the positive cones spanned by Teragaito's knots K_1,n and K_2,n are disjoint in the smooth concordance group 𝒞. For positive L-space knots, we show β completely determines the Alexander polynomial and distinguishes knots with identical Υ invariants.
ER  -