Plectis Atlas
Search

↑ and ↓ move, Enter opens, Esc closes.

Show on the map

Gersten’s conjecture and virtual compact specialness of one-relator groups

OpenAI groups related papers into a “family”. OpenAI’s catalogue describes this one:

Proves Gersten’s conjecture: every finitely generated one-relator group containing no Baumslag–Solitar subgroup \(\mathrm{BS}(m,n)\), with \(m,n\ne0\), is word-hyperbolic. It also proves that every word-hyperbolic one-relator group is virtually compact special.

The release has no Lean statement for this family, so there is no formal statement to compare with the result described above.

What the papers state

Theorem 1.1

In Virtual compact specialness of hyperbolic one-relator groups

The paper’s main theorem is shown as a possible match to OpenAI’s description. No review confirming the selection is recorded.

Let X be finite, let r\in F(X), and suppose that

G=F(X)/\langle\!\langle r\rangle\!\rangle

is word-hyperbolic. Then G is virtually compact special. More precisely, there are a finite-index subgroup H\leq G, a finite connected nonpositively curved cube complex C, and a finite simplicial graph \Lambda such that

\pi_1(C)\cong H \quad\text{and}\quad C\longrightarrow S_\Lambda

is a cubical local isometry to the Salvetti complex of the right-angled Artin group defined by \Lambda.

Theorem 1.2

In Virtual compact specialness of hyperbolic one-relator groups

Possible match to OpenAI’s description, selected because it shares the most wording. No review confirming the selection is recorded.

Let F be a finitely generated free group and let \phi:F\to F be injective. If its ascending mapping torus

F*_{\phi}=\langle F,t\mid t^{-1}ft=\phi(f),\ f\in F\rangle

is word-hyperbolic, then it is virtually compact special.

The release does not say which paper theorem its catalogue describes. Both statements above are shown whole: the paper’s main theorem first, then the statement that shares the most wording with the description. The atlas has not reviewed either choice.

Two more possible matches

  • Theorem 1.1 in Baumslag-Solitar-free one-relator groups are hyperbolic.
  • Theorem 1.2 in Baumslag-Solitar-free one-relator groups are hyperbolic.
Reported proof verification
The release has no Lean statement for this family. The papers are available to read and assess.
Papers and explanations
Two current papers, each readable here as a page beside its PDF.

Papers

Each paper opens as a reading page in the browser, with the PDF beside it. The statements each paper opens with are on its reading page.

Virtual compact specialness of hyperbolic one-relator groups

Undated, current edition.

Read it herePDF

We prove that every word-hyperbolic one-relator group is virtually compact special. Combined with the work of Kielak–Linton, this resolves Wise’s virtual free-by-cyclic conjecture for hyperbolic one-relator groups: every such group is virtually free-by-cyclic, with the free kernel allowed to have infinite rank.

Lean statements

The release has no Lean statement for this family. Its papers remain available to read, and contributors can propose a formal statement of a result. Suggest a change

Independent comparisons and proof-verification reports

Does the Lean express the advertised result?

The release contains no Lean statement for this family, so there is no formal statement to compare with OpenAI’s description.

What these papers cite in the release, and what cites them

These links come from the papers’ bibliographies. A citation records that one paper cites another; how each cited result is used has not been examined here.

Within this family

Papers elsewhere in the release that this family’s papers cite

This family’s papers cite no paper elsewhere in the release.

Papers elsewhere in the release that cite this family’s papers

No paper elsewhere in the release cites this family’s papers.

References outside the release

Each paper’s outside references are listed with it on its reading page, where each citation is placed. Every outside work cited in the release: References outside the release

Explain a result, compare statements or propose a correction

Atlas has no contributed explanation for this family yet. You can offer one with a GitHub account. You receive named credit and disclose any AI assistance.

Each button opens a GitHub form with this page and its source version filled in. Opening the form does not reserve the work.

Offer to write an explanationSuggest a source attributionSuggest a change

What people have said

Commentary on this family by others, dated and credited. It is commentary, not a finding.

  • An unsigned public tier list, the OpenAI Math Tier List, classes it as a proof and rates its significance, if it holds up, as “Major math journal”. The page says that nothing on it is verified.

    Author not stated. Source

Questions awaiting review

Each item identifies a statement, definition or report that needs further review. Its link opens a GitHub form with the source version already recorded.

Identify the theorem the catalogue describes

  • Family 258 The theorem shown was selected from shared wording with OpenAI’s description. Atlas records no review confirming that it is the theorem the description means. Open the form

State the result in Lean

  • Family 258 The release has no Lean statement for this family. Open the form