Morse theory for $G$-manifolds

Discrete Morse Theory for Manifolds with Boundary

We introduce a version of discrete Morse theory specific for manifolds with boundary. The idea is to consider Morse functions for which all boundary cells are critical. We obtain “Relative Morse Inequalities” relating the homology of the manifold to the number of interior critical cells. We also derive a Ball Theorem, in analogy to Forman’s Sphere Theorem. The main corollaries of our work are: ...

Two-orbit Kähler Manifolds and Morse Theory

We deal with compact Kähler manifolds M acted on by a compact Lie group K of isometries, whose complexification K has exactly one open and one closed orbit in M . If the K-action is Hamiltonian, we obtain results on the cohomology and the K-equivariant cohomology of M .

Classification of Two-dimensional Manifolds Using Morse Theory

Optimal discrete Morse functions for 2-manifolds

Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Mo...

Morse Theory