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Mapping class groups and outer automorphism groups of free groups are C*-simple

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Martin R. Bridson, Pierre de la Harpe

Operator Algebras · Submitted 12 Jun 2003

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

The authors' main claim We prove that the reduced C*-algebras of centerless mapping class groups and outer automorphism groups of free groups are simple, as are the irreducible pure subgroups of mapping class groups and the analogous subgroups of outer automorphism groups of free groups.

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arXiv IDmath/0306204 (version 1)
Pith IDEV5H36C3, Pith's permanent record of this paper and its review
CitationMartin R. Bridson, Pierre de la Harpe. "Mapping class groups and outer automorphism groups of free groups are C*-simple." arXiv:math/0306204 (2003). https://pith.science/paper/EV5H36C3
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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, 1,690 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We prove that the reduced C*-algebras of centerless mapping class groups and outer automorphism groups of free groups are simple, as are the irreducible pure subgroups of mapping class groups and the analogous subgroups of outer automorphism groups of free 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 prove that the reduced C*-algebras of centerless mapping class groups and outer automorphism groups of free groups are simple, as are the irreducible pure subgroups of mapping class groups and the analogous subgroups of outer automorphism groups of free groups. result 0.97 0.96 0.96 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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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 the reduced C*-algebras of centerless mapping class groups and outer automorphism groups of free groups are simple, as are the irreducible pure subgroups of mapping class groups and the analogous subgroups of outer automorphism groups of free groups.

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