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Tiling Spaces have aspherical shape

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Scott Schmieding

Dynamical Systems · Submitted 19 Nov 2015

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

The authors' main claim We show for dimensions greater than one that these groups are trivial.

how it is stated · asserted 1.00 read the record →

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arXiv ID1511.06154 (version 2)
Pith IDPMMTDBT5, Pith's permanent record of this paper and its review
CitationScott Schmieding. "Tiling Spaces have aspherical shape." arXiv:1511.06154 (2015). https://pith.science/paper/PMMTDBT5
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The compiled record

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, 3,611 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.29 · compares with prior results 0.85 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Going beyond the cohomological invariants attached to tiling spaces via inverse limit constructions, Clark and Hunton introduced shape group invariants, and showed these invariants in dimension one give new information. We show for dimensions greater than one that these groups are trivial. To do this, we show that the topological hull associated to a tiling in $\mathbb{R}^{d}$ is the inverse limit of aspherical branched manifolds. The result follows from work of Gromov and others on complete geodesic spaces of nonpositive Alexandrov curvature, along with some simple observations.

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 Going beyond the cohomological invariants attached to tiling spaces via inverse limit constructions, Clark and Hunton introduced shape group invariants, and showed these invariants in dimension one give new information. background 1.00 0.05 0.04 asserted 1.00
s1 We show for dimensions greater than one that these groups are trivial. result 1.00 0.96 0.78 asserted 1.00
s2 To do this, we show that the topological hull associated to a tiling in $\mathbb{R}^{d}$ is the inverse limit of aspherical branched manifolds. method 0.87 0.90 0.11 asserted 1.00
s3 The result follows from work of Gromov and others on complete geodesic spaces of nonpositive Alexandrov curvature, along with some simple observations. method 0.82 0.17 0.06 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • 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

Going beyond the cohomological invariants attached to tiling spaces via inverse limit constructions, Clark and Hunton introduced shape group invariants, and showed these invariants in dimension one give new information. We show for dimensions greater than one that these groups are trivial. To do this, we show that the topological hull associated to a tiling in $\mathbb{R}^{d}$ is the inverse limit of aspherical branched manifolds. The result follows from work of Gromov and others on complete geodesic spaces of nonpositive Alexandrov curvature, along with some simple observations.

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