Galois conjugates of pseudo-Anosov stretch factors are dense in the complex plane

Bal\'azs Strenner

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Galois conjugates of pseudo-Anosov stretch factors are dense in the complex plane

Balázs Strenner

Geometric Topology · Submitted 17 Feb 2017

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

The authors' main claim We show that - except in low-complexity cases - these conjugates are dense in the complex plane.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,234 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.86 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper, we study the Galois conjugates of stretch factors of pseudo-Anosov elements of the mapping class group of a surface. We show that - except in low-complexity cases - these conjugates are dense in the complex plane. For this, we use Penner's construction of pseudo-Anosov mapping classes. As a consequence, we obtain that in a sense there is no restriction on the location of Galois conjugates of stretch factors arising from Penner's construction. This complements an earlier result of Shin and the author stating that Galois conjugates of stretch factors arising from Penner's construction may never lie on the unit circle.

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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	In this paper, we study the Galois conjugates of stretch factors of pseudo-Anosov elements of the mapping class group of a surface.	contribution 0.67	0.83	0.03	unclear 0.56
s1	We show that - except in low-complexity cases - these conjugates are dense in the complex plane.	result 1.00	0.96	0.93	asserted 1.00
s2	For this, we use Penner's construction of pseudo-Anosov mapping classes.	method 1.00	0.46	0.03	asserted 0.97
s3	As a consequence, we obtain that in a sense there is no restriction on the location of Galois conjugates of stretch factors arising from Penner's construction.	interpretation 0.96	0.91	0.21	asserted 0.90
s4	This complements an earlier result of Shin and the author stating that Galois conjugates of stretch factors arising from Penner's construction may never lie on the unit circle.	background 0.84	0.28	0.05	hedged possibility 0.85

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

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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

In this paper, we study the Galois conjugates of stretch factors of pseudo-Anosov elements of the mapping class group of a surface. We show that - except in low-complexity cases - these conjugates are dense in the complex plane. For this, we use Penner's construction of pseudo-Anosov mapping classes. As a consequence, we obtain that in a sense there is no restriction on the location of Galois conjugates of stretch factors arising from Penner's construction. This complements an earlier result of Shin and the author stating that Galois conjugates of stretch factors arising from Penner's construction may never lie on the unit circle.

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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

What it cites · 7 sentences without a confident label

Builds on 1 paper

Penner's construction also works on nonorientable surfaces [ref] , and an analog of <Ref> could be proven also for sufficiently complicated nonorientable surfaces.

Algebraic degrees of pseudo-Anosov stretch factors · Nonorientable surfaces · 0.82

Cites as background 2 papers

Hamenstädt [ref] showed that (in an appropriate sense) typical stretch factors of the homological actions of pseudo-Anosov mapping classes are totally real.

Typical and atypical properties of periodic Teichmueller geodesics · Related results · 0.81
Thurston [ref] studied the stretch factors of graph maps, outer automorphisms of free groups and post-critically finite self-maps of the unit interval.

Entropy in Dimension One · Related results · 0.98

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