Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill topology-and-geometry-advancedgit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/topology-and-geometry-advanced)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/topology-and-geometry-advanced"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/topology-and-geometry-advanced/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/topology-and-geometry-advanced"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/topology-and-geometry-advanced.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00070 | $0.00620 |
| Opus 5.5 | $0.00028 | $0.00248 |
| Sonnet 5.5 | $0.00014 | $0.00124 |
| Haiku 4.5 | $0.00007 | $0.00062 |
Grade A, and why
topology-and-geometry-advanced scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 31 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Topology & Advanced Geometry
Point-set topology
- Topological space (open sets), basis, subspace/product/quotient topologies; closure, interior, boundary.
- Continuity = preimages of opens are open; homeomorphism; Hausdorff, regular, normal; metrizable.
- Compactness (every open cover has a finite subcover; Tychonoff product theorem), connectedness, path-connectedness; Urysohn lemma, Tietze extension.
- Examples: Zariski, order, cofinite, Sorgenfrey line, topologist's sine curve.
Algebraic topology
- Homotopy equivalence; fundamental group pi_1: pi_1(S^1) = Z, pi_1(torus) = Z^2; van Kampen theorem; covering spaces and the lifting criterion; classification of surfaces.
- Homology H_n (simplicial, singular, cellular): Betti numbers; Euler characteristic chi = sum (-1)^n b_n (sphere 2, torus 0); Mayer-Vietoris; cohomology and cup product; Poincare duality; Brouwer fixed-point theorem; Borsuk-Ulam; hairy ball theorem.
- Higher homotopy groups, fibrations, K-theory, spectral sequences (overview).
- Knot theory: Reidemeister moves, Jones polynomial, knot invariants. Topological data analysis: persistent homology.
Manifolds & differential geometry
- Smooth manifolds, charts, tangent spaces, vector fields, Lie bracket, differential forms, exterior derivative d, Stokes theorem, de Rham cohomology.
- Riemannian metric g, geodesics, Levi-Civita connection, curvature tensor, sectional/Ricci/scalar curvature; Gauss-Bonnet: integral K dA + boundary = 2 pi chi; Gauss's Theorema Egregium; Hopf-Rinow.
- Lie groups and Lie algebras; fiber bundles and connections (gauge theory link).
- Surfaces in R^3: first and second fundamental form, principal curvatures, minimal surfaces; Poincare conjecture (Perelman via Ricci flow).
Algebraic geometry (overview)
Affine varieties V(I), Nullstellensatz, Zariski topology, projective space, Bezout's theorem (intersection number = product of degrees), schemes, sheaves, elliptic curves, Riemann-Roch.
Intuition
Topology ignores distances: a coffee cup equals a donut; use invariants (pi_1, H_n, chi, orientability) to prove spaces are not equivalent.
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- today First seen · 31 lines · 70 tokens per session scan A 230945ed0ba1
topology-and-geometry-advanced is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 70 tokens to every session and 620 once invoked, about $0.0003 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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