Cyclic branched covers of alternating knots and $L$-spaces

Masakazu Teragaito

RECORD

Cyclic branched covers of alternating knots and $L$-spaces

Masakazu Teragaito

Geometric Topology · Submitted 28 Apr 2014

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

The authors' main claim We show that the three-fold cyclic branched cover is also an $L$-space for any genus one alternating knot.

how it is stated · asserted 1.00 read the record →

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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, 2,262 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.59 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.27 · compares with prior results 0.85 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

For any alternating knot, it is known that the double branched cover of the $3$-sphere branched over the knot is an $L$-space. We show that the three-fold cyclic branched cover is also an $L$-space for any genus one alternating knot.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	For any alternating knot, it is known that the double branched cover of the $3$-sphere branched over the knot is an $L$-space.	background 1.00	0.03	0.04	asserted 1.00
s1	We show that the three-fold cyclic branched cover is also an $L$-space for any genus one alternating knot.	result 0.80	0.96	0.90	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

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

For any alternating knot, it is known that the double branched cover of the $3$-sphere branched over the knot is an $L$-space. We show that the three-fold cyclic branched cover is also an $L$-space for any genus one alternating knot.

Human review

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How the literature uses it

1 arXiv paper cite this in 4 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 · 2 sentences without a confident label

Builds on it 1 paper

With this, we can improve [ref] to the following.

Taut foliations, left-orderability, and cyclic branched covers · Introduction · 0.92

Cites it as support 1 paper

That $Σ_3(K)$ is an L-space is proved in [ref] .

Taut foliations, left-orderability, and cyclic branched covers · Three-strand pretzel knots · 0.98

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