geometry-and-topology - SKILL.md Agent Skill

name: geometry-and-topology description: Use when targeting Geometry & Topology (Geom. Topol.) or deciding whether a geometry or topology manuscript fits this top-tier MSP journal. Encodes the journal's fit, framing, proof-and-rigor bar, house style, official-submission re-check, and desk-reject heuristics.

Geometry & Topology (geometry-and-topology)

Journal positioning

Geometry & Topology, published by Mathematical Sciences Publishers (MSP), is a top-tier journal for research in geometry and topology, broadly construed. Its defining character is depth and significance within these fields: it publishes major, fully rigorous contributions across differential, algebraic, symplectic, and geometric topology and geometry, low-dimensional topology, geometric group theory, gauge theory, and adjacent areas where geometric or topological ideas are central. It is community-run and highly regarded, and a paper is judged on the importance and correctness of its theorems and on the durability of the methods within geometry and topology, rather than on breadth across all of mathematics. Readership is the geometry-and-topology research community. This skill is a fit / venue-selection / re-framing tool. It does not replace the journal's current official submission guidelines or the editorial board's judgment. Before submitting, re-check the live author instructions on the Geometry & Topology / MSP site.

When to trigger

The author names Geometry & Topology as the target for a substantial, fully proved result in geometry or topology.
A manuscript advances low-dimensional topology, geometric group theory, symplectic/contact geometry, gauge theory, or geometric analysis, and the author is choosing between Geometry & Topology and Inventiones Mathematicae or JAMS.
A result is a major contribution within geometry and topology but may not have the cross-all-of-mathematics reach of an apex generalist venue.
The author needs Geometry & Topology's expectations on full rigor, exposition, and submission norms before committing.

Scope & topic fit

Low-dimensional topology: 3- and 4-manifolds, knot theory, mapping class groups, and related invariants.
Symplectic and contact geometry, Floer theory, and gauge theory, including Seiberg-Witten and instanton methods.
Geometric group theory: groups acting on spaces, hyperbolicity, boundaries, and large-scale geometry.
Algebraic and differential geometry where topological or geometric structure is central to the contribution.
Geometric analysis and geometric flows with topological consequences.
Homotopy theory, K-theory, and categorical or higher-structural methods applied to geometric/topological problems.

Method & evidence bar

Results must be complete and fully proved: every theorem established rigorously, with no gaps, no reliance on unpublished claims without proof, and no unverified computation passed off as established.
Significance within geometry and topology is required: the work must be an important advance or introduce methods of lasting influence in these fields, not an incremental variation.
Proofs must be referee-verifiable in full; technical lemmas are proved or precisely cited, and the architecture of long arguments is made clear to an expert reader.
The Mathematics Subject Classification (MSC) should be assigned accurately to situate the work for editors and referees.
arXiv posting is standard and encouraged in mathematics; there is no data- or code-deposition norm, but any computer-assisted proof or large computation must be documented for independent checking.
Prior and concurrent results must be credited precisely, and the advance over the state of the art stated exactly.

Structure & house style

Standard pure-mathematics structure: abstract, introduction stating the main theorems and their significance, preliminaries, the body of proofs, and references; length follows the needs of a complete, rigorous argument.
The introduction must state the main results precisely, explain their importance within geometry and topology, and relate them to prior work.
Exposition must be high quality: precise definitions, consistent notation, and proofs organized so the reader grasps the structure before the technical detail; figures are encouraged where geometry aids understanding.
Long arguments may be modularized into lemmas and propositions; routine verifications or auxiliary computations may go to appendices.
Theorem statements should be self-contained and quotable, with unambiguous hypotheses and conclusions.
LaTeX is expected; MSP has specific style and production conventions to follow.

Official-submission checklist

Before giving submission-ready advice, read ../../resources/source-basis.md and ../../resources/official-source-map.md; start from the official source anchors for this journal family, then cite the current journal-specific page you checked.
Search the live site for "Geometry & Topology MSP submission guidelines" and follow the current MSP version.
Re-check the submission procedure, file-format and LaTeX/MSP style requirements, and editor-handling conventions.
Re-check MSC classification requirements and the journal's expectations on exposition, figures, and length.
Re-check authorship, competing-interests, and any AI-use disclosure requirements; confirm arXiv/preprint posting policy and documentation expectations for computer-assisted proofs.
If the live official instructions conflict with this skill, the official instructions win.

Pre-submission self-check

One sentence — the main theorem and why it is an important advance within geometry and topology.
Every proof is complete and referee-verifiable, with all lemmas proved or precisely cited and no unverified computation.
The introduction states results precisely and positions them honestly against prior and concurrent work.
MSC classification is assigned accurately and figures clarify the geometry where helpful.
Any computer-assisted component is documented for independent verification; the preprint/arXiv status is consistent with policy.
The result's significance matches a top-tier geometry/topology venue, not merely a sound specialist contribution.

Common desk-reject triggers

A correct but incremental result that does not represent a major advance or introduce influential methods within geometry and topology.
A proof with gaps, hand-waved steps, or reliance on unproved claims or unverified computation.
Overstated significance or imprecise positioning relative to known results in the field.
A manuscript whose exposition is too disorganized for a referee to verify the argument.
Work whose core is outside geometry/topology, where a different specialist journal is the natural home.

Re-routing decision

A major advance with reach across all of mathematics, especially via geometry/arithmetic geometry: inventiones-mathematicae.
A field-shaping result of broad significance suited to a flagship society generalist venue: journal-of-the-american-mathematical-society.
An exceptional, all-mathematics-significance result: acta-mathematica or annals-of-mathematics.
A strong but more specialized topology/geometry result: the leading journal of the specific subfield.

Output format

[Fit] High / Medium / Low (one-line reason)
[Target] Geometry & Topology
[Topic tags] <2–3 closest areas / MSC themes>
[Method/evidence] <are the proofs complete and referee-verifiable, and is the result a major advance within geometry and topology?>
[Top risk] <the single most likely reason for rejection>
[Official items to re-check] <submission/LaTeX-MSP style / MSC classification / exposition, figures & length / arXiv & computer-proof documentation / disclosure>
[Re-route suggestion] <if not a fit, a better-matched venue>