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Mostow rigidity for Fuchsian buildings

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Xiangdong Xie

Group Theory · Submitted 23 Jul 2004

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

The authors' main claim It follows that Mostow rigidity holds for Fuchsian buildings: if a group acts properly and cocompactly on two Fuchsian buildings X and Y, then X and Y are equivariantly isomorphic.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0407394 (version 1)
Pith ID2PQZMRGI, Pith's permanent record of this paper and its review
CitationXiangdong Xie. "Mostow rigidity for Fuchsian buildings." arXiv:math/0407394 (2004). https://pith.science/paper/2PQZMRGI
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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, 2,362 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · 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; .

We show that if a homeomorphism between the ideal boundaries of two Fuchsian buildings preserves the combinatorial cross ratio almost everywhere, then it extends to an isomorphism between the Fuchsian buildings. It follows that Mostow rigidity holds for Fuchsian buildings: if a group acts properly and cocompactly on two Fuchsian buildings X and Y, then X and Y are equivariantly isomorphic.

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 show that if a homeomorphism between the ideal boundaries of two Fuchsian buildings preserves the combinatorial cross ratio almost everywhere, then it extends to an isomorphism between the Fuchsian buildings. result 0.94 0.93 0.50 asserted 1.00
s1 It follows that Mostow rigidity holds for Fuchsian buildings: if a group acts properly and cocompactly on two Fuchsian buildings X and Y, then X and Y are equivariantly isomorphic. interpretation 0.77 0.86 0.83 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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  • references and citing sentences
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  • P abstract
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  • 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 show that if a homeomorphism between the ideal boundaries of two Fuchsian buildings preserves the combinatorial cross ratio almost everywhere, then it extends to an isomorphism between the Fuchsian buildings. It follows that Mostow rigidity holds for Fuchsian buildings: if a group acts properly and cocompactly on two Fuchsian buildings X and Y, then X and Y are equivariantly isomorphic.

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