Surface
Critical Points:
Euler characteristic χ: —
χ = Σ (−1)^λᵢ where λ = Morse index
Euler characteristic χ: —
χ = Σ (−1)^λᵢ where λ = Morse index
Morse Lemma: Near a critical point, f ≈ −x₁²−⋯−x_λ²+x_{λ+1}²+⋯
Morse inequality: cₖ ≥ bₖ where bₖ = Betti numbers
Morse inequality: cₖ ≥ bₖ where bₖ = Betti numbers