# Nicolae Anghel
University of North Texas

## The Spectrum of the Dirac Operator on Certain
Topological Spheres

The spectral decomposition of the Dirac
operator on highly symmetrical spaces,
such as spheres, projective spaces, or grassmannians, is
completely understood. However,
the methods used to settle these cases, usually pertaining to
representation theory, are
inapplicable, if one looks at even the slightest geometric
perturbations of them, such as the ellipsoids
with circle symmetry in R^3, for instance. There
one must be satisfied with the various
bounds that exist on the spectrum.
In this talk, which represents work in progress, we will show
how classical methods can be used to
deal with the spectrum of the Dirac operator on a suitable
class of topological spheres, immersed in R^3.