Chain Complex

★★★★☆Undergraduate

📖Definition

Sequence of modules (or abelian groups) where composition of boundary maps is zero

📐Formulas

...→ Cₙ₊₁ →^∂ₙ₊₁ Cₙ →^∂ₙ Cₙ₋₁ →...
∂ₙ ∘ ∂ₙ₊₁ = 0
Hₙ(C) = ker ∂ₙ / im ∂ₙ₊₁

✏️Examples

예제 1

Simplicial complex

예제 2

Cellular complex

예제 3

de Rham complex

Applications

Topology

Algebraic geometry

Physics

🔗Related Documents

Related

Applications

#사슬#chain#복합체#complex