Proof — Morse theory and variational topology
Statement
Morse theory relates critical points of smooth functions on manifolds to topology via the Morse inequalities and handle decompositions.
Formula
Morse index; ∂²f positive definite
Equation
C_k ≅ free rank of critical points index k
Source
Canonical lineament aligned with TANAAKK IAS Faculty Emeriti index (2026); consult specialist monographs for full proofs.
Domains
mathematics