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Simplicial structures of knot complements

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Aleksandar Mijatovic

Geometric Topology · Submitted 6 Jun 2003

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

The authors' main claim In this paper we prove a generalisation of that result to all knot complements.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0306117 (version 1)
Pith IDILFNI3VH, Pith's permanent record of this paper and its review
CitationAleksandar Mijatovic. "Simplicial structures of knot complements." arXiv:math/0306117 (2003). https://pith.science/paper/ILFNI3VH
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,616 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.89 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

It was recently shown that there exists an explicit bound for the number of Pachner moves needed to connect any two triangulation of any Haken 3-manifold which contains no fibred sub-manifolds as strongly simple pieces of its JSJ-decomposition. In this paper we prove a generalisation of that result to all knot complements. The explicit formula for the bound is in terms of the numbers of tetrahedra in the two triangulations. This gives a conceptually trivial algorithm for recognising any knot complement among all 3-manifolds.

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 It was recently shown that there exists an explicit bound for the number of Pachner moves needed to connect any two triangulation of any Haken 3-manifold which contains no fibred sub-manifolds as strongly simple pieces of its JSJ-decomposition. background 1.00 0.04 0.06 asserted 1.00
s1 In this paper we prove a generalisation of that result to all knot complements. contribution 0.97 0.94 0.70 asserted 1.00
s2 The explicit formula for the bound is in terms of the numbers of tetrahedra in the two triangulations. result 0.84 0.85 0.12 asserted 1.00
s3 This gives a conceptually trivial algorithm for recognising any knot complement among all 3-manifolds. interpretation 0.98 0.79 0.18 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
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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

It was recently shown that there exists an explicit bound for the number of Pachner moves needed to connect any two triangulation of any Haken 3-manifold which contains no fibred sub-manifolds as strongly simple pieces of its JSJ-decomposition. In this paper we prove a generalisation of that result to all knot complements. The explicit formula for the bound is in terms of the numbers of tetrahedra in the two triangulations. This gives a conceptually trivial algorithm for recognising any knot complement among all 3-manifolds.

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