A Generalized Morse Theory

  title={A Generalized Morse Theory},
  author={Richard Palais and Stephen Smale},
1. Abstract theory. Let M be a C-Riemannian manifold without boundary modeled on a separable Hubert space (see Lang [3]). For pÇzM we denote by ( , )p the inner product in the tangent space Mp and we define a function || || on the tangent bundle T(M) by ||z>|| = (v, v)J for vÇzMp. Given p and q in the same component of M we define p(p, q)==lnïfl\\<r'(t)\\dtt where the Inf is over all C 1 paths <r\ [0, l]—>ikf such that a(0)=p and cr(l)=g. Just as in the finite dimensional case one shows that p… CONTINUE READING