Morse theory on Banach manifolds

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 .

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: ...

Measures on Banach Manifolds and Supersymmetric Quantum Field Theory

We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum field theory. We give three concrete examples of our construction. The first example is a family μ P of measures on a space of functions on the two-to...

The Morse Lemma on Banach Spaces

Let /: U-*R be a C3 map of an open subset U of a Banach space E. Letp £ U be a critical point of/ (df¡,=0). If £ is a conjugate space (E=F*) we define what it means for/» to be nondegenerate. In this case there is a diffeomorphism y of a neighborhood of p with a neighborhood of 0 E E, y(p)=0 with foy->(x) = id%(x,x)+f(p). In this paper we define a notion of nondegeneracy for critical points of ...

Classification of Two-dimensional Manifolds Using Morse Theory