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Cable links and L-space surgeries

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Eugene Gorsky, Jennifer Hom

Geometric Topology · Submitted 18 Feb 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that for m, n relatively prime, the r-component cable link $K_{rm,rn}$ is an L-space link if and only if K is an L-space knot and $n/m \geq 2g(K)-1$.

how it is stated · asserted 1.00 read the record →

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arXiv ID1502.05425 (version 2)
Pith ID5JFKDTXW, Pith's permanent record of this paper and its review
CitationEugene Gorsky, Jennifer Hom. "Cable links and L-space surgeries." arXiv:1502.05425 (2015). https://pith.science/paper/5JFKDTXW
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,613 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.89 · compares with prior results 0.25 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

An L-space link is a link in $S^3$ on which all sufficiently large integral surgeries are L-spaces. We prove that for m, n relatively prime, the r-component cable link $K_{rm,rn}$ is an L-space link if and only if K is an L-space knot and $n/m \geq 2g(K)-1$. We also compute HFL-minus and HFL-hat of an L-space cable link in terms of its Alexander polynomial. As an application, we confirm a conjecture of Licata regarding the structure of HFL-hat for (n,n) torus links.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 An L-space link is a link in $S^3$ on which all sufficiently large integral surgeries are L-spaces. background 1.00 0.05 0.04 asserted 0.99
s1 We prove that for m, n relatively prime, the r-component cable link $K_{rm,rn}$ is an L-space link if and only if K is an L-space knot and $n/m \geq 2g(K)-1$. result 0.99 0.96 0.84 asserted 1.00
s2 We also compute HFL-minus and HFL-hat of an L-space cable link in terms of its Alexander polynomial. result 0.91 0.95 0.09 asserted 1.00
s3 As an application, we confirm a conjecture of Licata regarding the structure of HFL-hat for (n,n) torus links. result 0.86 0.92 0.08 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
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  • figures and tables
  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

An L-space link is a link in $S^3$ on which all sufficiently large integral surgeries are L-spaces. We prove that for m, n relatively prime, the r-component cable link $K_{rm,rn}$ is an L-space link if and only if K is an L-space knot and $n/m \geq 2g(K)-1$. We also compute HFL-minus and HFL-hat of an L-space cable link in terms of its Alexander polynomial. As an application, we confirm a conjecture of Licata regarding the structure of HFL-hat for (n,n) torus links.

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3 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Compares with it 1 paper
  • For example, it is proved in [ref] that the point $(pq+1,…,pq+1)$ satisfies the conditions of Theorem [ref] for the $(pn,qn)$ torus link, while in the above bound one has $D_i=(npq-p-q)/2$ for $n>2$.

    Immersed concordances of links and Heegaard Floer homology · L-spaces and L-space links · 0.95

Cites it as background 1 paper

What it cites · 17 sentences without a confident label

Uses the method or tool of 2 papers
Cites as support 1 paper
  • If $K_rm, rn$ is an L-space link, then by [ref] all its components are L-space knots.

    $L$-space surgeries on links · Dehn surgery and cable links · 0.98

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