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Guts and volume for hyperbolic $3$-orbifolds with underlying space $S^3$

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Christopher K. Atkinson, Jessica Mallepalle, Joseph Melby, Shawn Rafalski, Jennifer Vaccaro

Geometric Topology · Submitted 12 Mar 2017

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

The authors' main claim For a hyperbolic $3$-orbifold with underlying space the $3$-sphere, we obtain a lower bound on its volume in the case that it contains an essential $2$-suborbifold with underlying space the $2$-sphere with four cone points.

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arXiv ID1703.04160 (version 1)
Pith IDHMQBMNUD, Pith's permanent record of this paper and its review
CitationChristopher K. Atkinson, Jennifer Vaccaro, Jessica Mallepalle, Joseph Melby, Shawn Rafalski. "Guts and volume for hyperbolic $3$-orbifolds with underlying space $S^3$." arXiv:1703.04160 (2017). https://pith.science/paper/HMQBMNUD
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,985 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.41 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.65 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

For a hyperbolic $3$-orbifold with underlying space the $3$-sphere, we obtain a lower bound on its volume in the case that it contains an essential $2$-suborbifold with underlying space the $2$-sphere with four cone points. Our techniques involve computing the guts of the orbifold split along the $2$-suborbifold via a careful analysis of its topology. We also characterize the orbifolds of this type that have empty guts.

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 For a hyperbolic $3$-orbifold with underlying space the $3$-sphere, we obtain a lower bound on its volume in the case that it contains an essential $2$-suborbifold with underlying space the $2$-sphere with four cone points. result 0.96 0.93 0.88 asserted 1.00
s1 Our techniques involve computing the guts of the orbifold split along the $2$-suborbifold via a careful analysis of its topology. method 1.00 0.94 0.04 asserted 0.99
s2 We also characterize the orbifolds of this type that have empty guts. result 0.88 0.94 0.10 asserted 1.00

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

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  • T body sentences
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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

For a hyperbolic $3$-orbifold with underlying space the $3$-sphere, we obtain a lower bound on its volume in the case that it contains an essential $2$-suborbifold with underlying space the $2$-sphere with four cone points. Our techniques involve computing the guts of the orbifold split along the $2$-suborbifold via a careful analysis of its topology. We also characterize the orbifolds of this type that have empty guts.

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