Simplicial Homology
Mode: Add Vertices
Euler Characteristic
V: 0 E: 0 F: 0
χ = β₀ − β₁ + β₂ = 0
Betti Numbers
β₀ = 0 (components)
β₁ = 0 (loops)
β₂ = 0 (voids)
Click to add simplices:
• Vertex mode: click canvas
• Edge mode: click 2 vertices
• Triangle mode: click 3 vertices
Homology via Smith normal form of boundary matrices ∂₁, ∂₂.
β₀ = rank ker ∂₀
β₁ = rank ker ∂₁ − rank im ∂₂
β₂ = rank ker ∂₂