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The adjunction problem over torsion-free groups

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Max Forester, Colin Rourke

Group Theory · Submitted 14 Dec 2004

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

The authors' main claim In this note we prove injectivity and relative asphericity for "layered" systems of equations over torsion-free groups, when the exponent matrix is invertible over Z.

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arXiv IDmath/0412274 (version 2)
Pith IDNUDIAFCO, Pith's permanent record of this paper and its review
CitationColin Rourke, Max Forester. "The adjunction problem over torsion-free groups." arXiv:math/0412274 (2004). https://pith.science/paper/NUDIAFCO
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,284 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.37 · mentions code or data availability 0.01.

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

In this note we prove injectivity and relative asphericity for "layered" systems of equations over torsion-free groups, when the exponent matrix is invertible over Z. We also give elementary geometric proofs of results due to Bogley-Pride and Serre that are used in the proof of the main theorem.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this note we prove injectivity and relative asphericity for "layered" systems of equations over torsion-free groups, when the exponent matrix is invertible over Z. result 0.68 0.96 0.93 asserted 1.00
s1 We also give elementary geometric proofs of results due to Bogley-Pride and Serre that are used in the proof of the main theorem. contribution 0.75 0.90 0.05 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

In this note we prove injectivity and relative asphericity for "layered" systems of equations over torsion-free groups, when the exponent matrix is invertible over Z. We also give elementary geometric proofs of results due to Bogley-Pride and Serre that are used in the proof of the main theorem.

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