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Incompressible surfaces in link complements

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Ying-Qing Wu

Geometric Topology · Submitted 1 Nov 2000

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

The authors' main claim We generalize a theorem of Finkelstein and Moriah and show that if a link $L$ has a $2n$-plat projection satisfying certain conditions, then its complement contains some closed essential surfaces.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0011006 (version 1)
Pith IDGSTIDEXL, Pith's permanent record of this paper and its review
CitationYing-Qing Wu. "Incompressible surfaces in link complements." arXiv:math/0011006 (2000). https://pith.science/paper/GSTIDEXL
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The compiled record

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,275 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.59 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.73 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We generalize a theorem of Finkelstein and Moriah and show that if a link $L$ has a $2n$-plat projection satisfying certain conditions, then its complement contains some closed essential surfaces. In most cases these surfaces remain essential after any totally nontrivial surgery on $L$.

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 We generalize a theorem of Finkelstein and Moriah and show that if a link $L$ has a $2n$-plat projection satisfying certain conditions, then its complement contains some closed essential surfaces. result 0.61 0.93 0.85 asserted 1.00
s1 In most cases these surfaces remain essential after any totally nontrivial surgery on $L$. result 0.99 0.81 0.21 asserted 0.76

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
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
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  • 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

We generalize a theorem of Finkelstein and Moriah and show that if a link $L$ has a $2n$-plat projection satisfying certain conditions, then its complement contains some closed essential surfaces. In most cases these surfaces remain essential after any totally nontrivial surgery on $L$.

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