MORSE THEORY AND STABILITY BY LIAPUNOV'S DIRECT METHOD

Stability for Holomorphic Spheres and Morse Theory

In this paper we study the question of when does a closed, simply connected, integral symplectic manifold (X,ω) have the stability property for its spaces of based holomorphic spheres? This property states that in a stable limit under certain gluing operations, the space of based holomorphic maps from a sphere to X, becomes homotopy equivalent to the space of all continuous maps, lim −→Holx0 (P...

Linking and Morse Theory

A. In this paper we use Morse theory and the gradient flow of a Morse-Smale function to compute the linking number of a two-component link L in S 3 , by counting the signed number of gradient flow lines passing through each component of L. We will also use three Morse-Smale functions and their gradient flows, to compute Milnor's triple linking number of three-component links by counting ...

Supersymmetry and Morse Theory

It is shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian. Some of the implications of modern ideas in mathematics for supersymmetric theories are discussed.

Morse Theory

Morse Theory and Evasiveness

x0. Introduction. Consider a game played by 2 players, whom we call the hider and the seeker. Let S be a simplex of dimension n, with vertices x 0 , x 1 ; : : :; x n , and M a subcomplex of S, known to both the hider and the seeker. Let be a simplex of S, known only to the hider. The seeker is permitted to ask questions of the sort \Is vertex x i in ?" The seeker's goal is to determine whether ...