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Weakly bounded cohomology classes and a counterexample to a conjecture of Gromov

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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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Dario Ascari, Francesco Milizia

Group Theory · Submitted 8 Jul 2022

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

The authors' main claim We exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class.

how it is stated · asserted 1.00 read the record →

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arXiv ID2207.03972 (version 2)
Pith ID7S3HHEGX, Pith's permanent record of this paper and its review
CitationDario Ascari, Francesco Milizia. "Weakly bounded cohomology classes and a counterexample to a conjecture of Gromov." arXiv:2207.03972 (2022). https://pith.science/paper/7S3HHEGX
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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, 2,265 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.30 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal covers of closed manifolds.

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 exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class. result 0.82 0.96 0.84 asserted 1.00
s1 As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal covers of closed manifolds. result 0.78 0.94 0.41 asserted 1.00

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

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

We exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal covers of closed manifolds.

Human review

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How the literature uses it

2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 10 sentences without a confident label

Uses the method or tool of 1 paper
  • To prove this claim, we use [ref] , that characterizes the kernel of $ι_CW$ in terms of a linear isoperimetric inequality: $ι_CW([α_]) = 0$ if and only if there is a constant $L ∈$ such that $α_(c) ≤L∂c_1$ for every $c ∈C_2^CW(X;)$.

    2107.09089 · A weakly bounded but not bounded class · 0.86

Cites as support 1 paper
  • The first of the two facts follows directly from the definitions, while the second one is proved in [ref] .

    Central extensions and bounded cohomology · Bounded cohomology and L-infinity-cohomology · 0.96

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