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
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#사슬#chain#복합체#complex