---
title: De Rham Cohomology
description: De Rham cohomology uses differential forms to study the topological shape of smooth manifolds. Learners will understand how to compute cohomology groups, detect topological holes, and relate analytic properties to global geometric structures.
category: mathematics
subcategory: differential-topology
difficulty: beginner, intermediate, advanced
url: /subject/de-rham-cohomology
---

# De Rham Cohomology

De Rham cohomology uses differential forms to study the topological shape of smooth manifolds. Learners will understand how to compute cohomology groups, detect topological holes, and relate analytic properties to global geometric structures.

## Available Resources

4 Websites

## Websites

### 1. MathOverflow: Learning de Rham cohomology

Thread with expert recommendations, cross-posted to Reddit.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://mathoverflow.net/questions/12345/learning-de-rham-cohomology

### 2. nLab: de Rham cohomology

Comprehensive reference with definitions and references, frequently linked in Reddit discussions.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://ncatlab.org/nlab/show/de+Rham+cohomology

**Tags:** de-rham-cohomology, differential-forms, algebraic-topology, differential-geometry

### 3. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

### 4. nLab

Collaborative wiki for mathematics, physics and philosophy written from a category-theoretic viewpoint, with cross-linked entries on categories, functors, adjunctions, topos theory, higher category theory and homotopy theory. Readers can look up precise definitions, examples and references for advanced structural mathematics.

**Difficulty:** Advanced | **Language:** English | **Price:** Free

**Link:** https://ncatlab.org

**Tags:** category-theory, higher-category-theory, topos-theory, homotopy-theory, reference-wiki

---

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