Morse function f: M→ℝ with non-degenerate critical pts. Level-set topology changes at critical values; M built from cells of dim = Morse index. Bott.
Morse theory
Related concepts
- h-cobordism theorem
- Smooth manifold
- Morse theory: critical-point indices, handle-attachment, Morse inequalities
- Paraboloid f=x²−y²: grad(0)=0; Hessian diag(2,−2); det −4; Morse index 1
- Height on S²: perfect Morse, c=(1,0,1), Σ(−1)^i c_i = χ(S²) = 2
- Kondo one-loop RG: scaling equation dJ/d ln(Lambda) = -rho J^2; dynamical scale T_K = Lambda_0 exp(-1/(2 rho J_0))