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The proper geometric dimension of the mapping class group of an orientable surface with punctures

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Nestor Colin, Rita Jiménez Rolland, Porfirio L. León Álvarez, Luis Jorge Sánchez Saldaña

Geometric Topology · Submitted 18 Dec 2024

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

The authors' main claim We show that the {\it full} mapping class group of any orientable closed surface with punctures admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension.

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arXiv ID2412.14410 (version 1)
Pith ID5YFRSJGG, Pith's permanent record of this paper and its review
CitationLuis Jorge S\'anchez Salda\~na, Nestor Colin, Porfirio L. Le\'on \'Alvarez, Rita Jim\'enez Rolland. "The proper geometric dimension of the mapping class group of an orientable surface with punctures." arXiv:2412.14410 (2024). https://pith.science/paper/5YFRSJGG
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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, 2,959 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.58 · compares with prior results 0.94 · 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 the {\it full} mapping class group of any orientable closed surface with punctures admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension. This was proved for closed orientable surfaces and for {\it pure} mapping class groups by Aramayona and Mart\'inez P\'erez. As a consequence of our result we also obtain the proper geometric dimension of {\it full} spherical braid groups.

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 the {\it full} mapping class group of any orientable closed surface with punctures admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension. result 0.88 0.96 0.95 asserted 1.00
s1 This was proved for closed orientable surfaces and for {\it pure} mapping class groups by Aramayona and Mart\'inez P\'erez. background 0.95 0.03 0.04 asserted 1.00
s2 As a consequence of our result we also obtain the proper geometric dimension of {\it full} spherical braid groups. result 0.77 0.91 0.08 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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  • references and citing sentences
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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 show that the {\it full} mapping class group of any orientable closed surface with punctures admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension. This was proved for closed orientable surfaces and for {\it pure} mapping class groups by Aramayona and Mart\'inez P\'erez. As a consequence of our result we also obtain the proper geometric dimension of {\it full} spherical braid groups.

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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

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