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Algebraic and combinatorial codimension-1 transversality

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Andrew Ranicki

Algebraic Topology · Submitted 12 Aug 2003

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

The authors' main claim The Waldhausen construction of Mayer-Vietoris splittings of chain complexes over an injective generalized free product of group rings is extended to a combinatorial construction of Seifert-van Kampen splittings of CW complexes with fundamental group an injective generalized free product.

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arXiv IDmath/0308111 (version 3)
Pith ID5SG7M5BQ, Pith's permanent record of this paper and its review
CitationAndrew Ranicki. "Algebraic and combinatorial codimension-1 transversality." arXiv:math/0308111 (2003). https://pith.science/paper/5SG7M5BQ
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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, 1,696 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.54 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The Waldhausen construction of Mayer-Vietoris splittings of chain complexes over an injective generalized free product of group rings is extended to a combinatorial construction of Seifert-van Kampen splittings of CW complexes with fundamental group an injective generalized free product.

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 The Waldhausen construction of Mayer-Vietoris splittings of chain complexes over an injective generalized free product of group rings is extended to a combinatorial construction of Seifert-van Kampen splittings of CW complexes with fundamental group an injective generalized free product. contribution 0.99 0.84 0.78 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.52 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v3
not examined
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  • figures and tables
  • 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

The Waldhausen construction of Mayer-Vietoris splittings of chain complexes over an injective generalized free product of group rings is extended to a combinatorial construction of Seifert-van Kampen splittings of CW complexes with fundamental group an injective generalized free product.

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