Year: 2009
Type: preprint
Abstract: This is a survey article on a known generalization of Dirac-type operators to transverse operators called basic Dirac operators on Riemannian foliations, which are smooth foliations that have a transverse geometric structure. Construction of these operators requires the additional structure of what is called a bundle-like metric. We explain the result by Habib-R. that the spectrum of such an operator is independent of the choice of bundle-like metric, provided that the transverse geometric structure is fixed. We discuss consequences, which include defining a new version of the exterior derivative and de Rham cohomology that are nicely adapted to this transverse geometric setting.
Source: arXiv (Cornell University)
Author: Richardson, Ken
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W101216498