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The Weil-Petersson Isometry Group

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Howard Masur, Michael Wolf

Differential Geometry · Submitted 8 Aug 2000

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

The authors' main claim We prove that every Weil-Petersson isometry of the Teichmuller space T(g,n) is induced by an element of the extended mapping class group; here 3g-3+n > 1 and (g,n) is not (1,2).

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arXiv IDmath/0008065 (version 2)
Pith IDGJK5OHVA, Pith's permanent record of this paper and its review
CitationHoward Masur, Michael Wolf. "The Weil-Petersson Isometry Group." arXiv:math/0008065 (2000). https://pith.science/paper/GJK5OHVA
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,063 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.71 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.89 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We prove that every Weil-Petersson isometry of the Teichmuller space T(g,n) is induced by an element of the extended mapping class group; here 3g-3+n > 1 and (g,n) is not (1,2). Our method follows Ivanov's proof of the Royden's analogous theorem for the Teichmuller metric: we study the action of an isometry on the frontier of the metric completion of the Teichmuller space, and show that the isometry then induces an automorphism on the relevant complex of curves. Some synthetic geometry of the Weil-Petersson metric completes the proof.

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 prove that every Weil-Petersson isometry of the Teichmuller space T(g,n) is induced by an element of the extended mapping class group; here 3g-3+n > 1 and (g,n) is not (1,2). result 0.99 0.97 0.97 asserted 1.00
s1 Our method follows Ivanov's proof of the Royden's analogous theorem for the Teichmuller metric: we study the action of an isometry on the frontier of the metric completion of the Teichmuller space, and show that the isometry then induces an automorphism on the relevant complex of curves. method 1.00 0.80 0.03 asserted 0.99
s2 Some synthetic geometry of the Weil-Petersson metric completes the proof. method 0.96 0.79 0.02 asserted 0.97

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
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  • 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

We prove that every Weil-Petersson isometry of the Teichmuller space T(g,n) is induced by an element of the extended mapping class group; here 3g-3+n > 1 and (g,n) is not (1,2). Our method follows Ivanov's proof of the Royden's analogous theorem for the Teichmuller metric: we study the action of an isometry on the frontier of the metric completion of the Teichmuller space, and show that the isometry then induces an automorphism on the relevant complex of curves. Some synthetic geometry of the Weil-Petersson metric completes the proof.

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