Morse theory and asymptotic linear Hamiltonian system

Piecewise Linear Morse Theory

Classical Morse Theory [8] considers the topological changes of the level sets Mh = {x ∈ M | f(x) = h } of a smooth function f defined on a manifold M as the height h varies. At critical points, where the gradient of f vanishes, the topology changes. These changes can be classified locally, and they can be related to global topological properties of M . Between critical values, the level sets v...

Asymptotic Morse Theory for the Equation ∆ v = 2 vx ∧

Given a smooth bounded domain Ω ⊆ R, we consider the equation ∆v = 2vx ∧ vy in Ω, where v : Ω → R. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. C...

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