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topology-geometry-guide skill

/skills/mathematics/topology-geometry-guide

This skill helps you organize and accelerate topology and geometry research using structured modules, checklists, and knowledge graphs for up-to-date insights.

npx playbooks add skill sandraschi/advanced-memory-mcp --skill topology-geometry-guide

Review the files below or copy the command above to add this skill to your agents.

Files (6)
SKILL.md
1.2 KB
---
name: topology-and-geometry-guide
description: Expert in point-set topology, algebraic topology, differential geometry, and geometric intuition for abstract concepts
license: Proprietary
---

# Topology and Geometry Guide
> **Status**: ⚠️ Legacy template awaiting research upgrade
> **Last validated**: 2025-11-08
> **Confidence**: 🔴 Low — Legacy template awaiting research upgrade

## How to use this skill
1. Start with [modules/research-checklist.md](modules/research-checklist.md) and capture up-to-date sources.
2. Review [modules/known-gaps.md](modules/known-gaps.md) and resolve outstanding items.
3. Load topic-specific modules from [_toc.md](_toc.md) only after verification.
4. Update metadata when confidence improves.

## Module overview
- [Core guidance](modules/core-guidance.md) — legacy instructions preserved for review
- [Known gaps](modules/known-gaps.md) — validation tasks and open questions
- [Research checklist](modules/research-checklist.md) — mandatory workflow for freshness

## Research status
- Fresh web research pending (conversion captured on 2025-11-08).
- Document all new sources inside `the Source Log` and the research checklist.
- Do not rely on this skill until confidence is upgraded to `medium` or `high`.

Overview

This skill is an expert guide for point-set topology, algebraic topology, and differential geometry, focused on geometric intuition for abstract concepts. It provides structured guidance for studying, validating sources, and resolving known gaps, but currently requires research updates before being relied on for novel results. Use it as a curated roadmap and checklist for building dependable, referenced topology and geometry content.

How this skill works

The skill inspects conceptual dependencies across topology and geometry, highlights open validation tasks, and organizes a research workflow to refresh sources and fill gaps. It presents legacy guidance preserved for review and a prioritized checklist for capturing up-to-date references and documenting validation steps. Users should update metadata and confidence levels after completing research tasks.

When to use it

  • When assembling a learning or reference roadmap for topology and differential geometry
  • Before publishing educational material that requires verified references
  • When auditing existing notes or a knowledge base for missing proofs or citations
  • When coordinating research work to bring legacy content up to current standards
  • When you need a prioritized checklist to validate and update mathematical content

Best practices

  • Start by capturing current primary sources and landmark references for each topic
  • Document every new source in a central source log with provenance and notes
  • Resolve known gaps by prioritizing foundational results before advanced topics
  • Use small, verifiable validation tasks and mark confidence levels as you complete them
  • Keep geometric intuition and formal statements paired to aid comprehension

Example use cases

  • Creating a vetted study plan for a graduate course on differential geometry
  • Auditing a personal knowledge repository to identify and fix missing proofs
  • Preparing lecture notes that link intuition, examples, and rigorous statements
  • Coordinating a small team to update legacy content with modern references
  • Converting informal geometric explanations into formal, referenced writeups

FAQ

Is the content ready for citation in research or teaching?

Not yet; the skill flags itself as legacy and requires fresh research and validation before being used as a primary citation source.

What should I do first to improve confidence?

Capture recent authoritative sources, document them in a source log, and complete the prioritized validation checklist to raise the confidence level.