Tags: #projects/notes/reading #geomtop/symplectic-topology Refs: Unsorted/Stein

Stein Manifolds

Goal: set up Stein and Weinstein cobordisms, get a Weinstein analog of the h-cobordism theorem.

Supporting concepts

• Normal forms of functions near critical points

• Vector fields near zeros (?)

• Lyapunov pair : a function and a gradient-like vector field

• Smale cobordisms and homotopies

• Elementary cobordisms

• Profiles and holonomy

• Review Classical h-cobordism theorem

• Morse Lemma : Nondegenerate index \(k\) for \(\phi: M^n \to {\mathbf{R}}\) implies \(\phi(u) = \phi(p) - \mathbf{u}_k^t A \mathbf{u}_{n-k}\)

• Definitions: embryonic, birth-death types, Cerf diagram

• Theorem: Critical points in 1-parameter families of diffeos are nondegenerate and only birth-death type

• Definition: Morse index

• Definition: Stable and unstable manifolds

• Definition: Lyapnuov functions