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A formula for the Whitehead group of a three-dimansional crystallographic group

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A. Alves, P. Ontaneda

K-Theory and Homology · Submitted 10 Oct 2003

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

The authors' main claim We give an explicit formula for Whitehead group of a three-dimensional crystallographic group in terms of the Whitehead groups of its virtually infinite cyclic subgroups.

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arXiv IDmath/0310156 (version 1)
Pith IDX4HJJCDG, Pith's permanent record of this paper and its review
CitationA. Alves, P. Ontaneda. "A formula for the Whitehead group of a three-dimansional crystallographic group." arXiv:math/0310156 (2003). https://pith.science/paper/X4HJJCDG
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,633 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We give an explicit formula for Whitehead group of a three-dimensional crystallographic group in terms of the Whitehead groups of its virtually infinite cyclic subgroups.

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 give an explicit formula for Whitehead group of a three-dimensional crystallographic group in terms of the Whitehead groups of its virtually infinite cyclic subgroups. contribution 0.80 0.95 0.94 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 give an explicit formula for Whitehead group of a three-dimensional crystallographic group in terms of the Whitehead groups of its virtually infinite cyclic subgroups.

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