17 pages matching lower level sets in this book
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Morse Theory without constraints
Morse Theory with constraints
3 other sections not shown
assume boundary Chebyshev approximation compact Condition C w.r.t. connected components Consequently consider continuous map convex coordinate system Corollary defined denote Df(x diffeomorphism eigenvalues equivalence Example f a,b fact follows fulfils Condition function f global minimum H X,A hence homeomorphic homotopy type homotopy-equivalence implies induced isomorphism k-dimensional Ker h Kuhn-Tucker point Let f linear subspace lower level sets m+p+1 manifold map F matrix minimum for f Moreover Morse Theory nondegenerate critical point nonempty nonsingular Note obtain Obviously one-parameter group open neighborhood open set open subset pair-map partition of unity path-connected point for f positive definite positive semi-definite proof of Theorem prove q q q quadratic index relative interior Remark resp Section set E(x set f singular strong deformation retract sufficiently small Suppose surjective tangent topological topological space trajectory unique vector vectorfield view of Lemma yields