Finite volume flows and Morse theory
By F. R. Harvey, H. Lawson, Jr.. 2001
57 citations recorded by the source corpus.
In this paper we present a new approach to Morse theory based on the de Rham-Federer theory of currents. The full classical theory is derived in a transparent way. The methods carry over uniformly to the equivariant and the holomorphic settings. Moreover, the methods are substantially stronger than the classical ones and have interesting applications to geometry. They lead, for example, to formulas relating characteristic forms and singularities of bundle maps.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3fd06b86cb5423a7b82cf0e55143fcb543cbe5df
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Microlocal branes are constructible sheaves (2006, background): “In turn, following arguments of [12], [23], homological perturbation theory provides a quasi-equivalence between the Morse A∞-composition structure and the dg structure given by the wedge product of forms.”
- Homological mirror symmetry and torus fibrations (2000, methodology): “Our proof of the equivalence of Morse and de Rham A∞-categories uses the approach to Morse theory from [ HL ].”
- Constructible sheaves and the Fukaya category (2006, result): “The construction of the idempotent and the homotopy is completely analogous to that of Kontsevich-Soibelman: one composes the limit operators of Harvey-Lawson [15] with a smoothing operator.”