HYPERCLASS FORCING IN MORSE-KELLEY CLASS THEORY

Morse Theory

Persistence in discrete Morse theory

Stratified Morse Theory in Arrangements

This paper is a survey of our work based on the stratified Morse theory of Goresky and MacPherson. First we discuss the Morse theory of Euclidean space stratified by an arrangement. This is used to show that the complement of a complex hyperplane arrangement admits a minimal cell decomposition. Next we review the construction of a cochain complex whose cohomology computes the local system cohom...

Morse Theory on Graphs

Let Γ be a finite d-valent graph and G an n-dimensional torus. An " action " of G on Γ is defined by a map which assigns to each oriented edge, e, of Γ, a one-dimensional representation of G (or, alternatively, a weight, αe, in the weight lattice of G. For the assignment, e → αe, to be a schematic description of a " G-action " , these weights have to satisfy certain compatibility conditions: th...

Morse Theory on Meshes

In this report, we discuss two papers that deal with computing Morse function on triangulated manifolds. Axen [1] gives an algorithm for computing Morse function on a triangulated manifold of arbitrary dimension but it not practical because of its space requirement. Hence, he describes an algorithm for computing critical points and their Morse indices for a 2-manifold. Edelsbrunner et al. [2] d...