4,272 research outputs found
A Remark on Gelfand Duality for Spectral Triples
We present a duality between the category of compact Riemannian spin
manifolds (equipped with a given spin bundle and charge conjugation) with
isometries as morphisms and a suitable "metric" category of spectral triples
over commutative pre-C*-algebras. We also construct an embedding of a
"quotient" of the category of spectral triples introduced in
arXiv:math/0502583v1 into the latter metric category. Finally we discuss a
further related duality in the case of orientation and spin-preserving maps
between manifolds of fixed dimension.Comment: 15 pages, AMS-LaTeX2e, results unchanged, several improvements in the
exposition, appendix adde
Bounded geometry, growth and topology
We characterize functions which are growth types of Riemannian manifolds of
bounded geometry.Comment: 15 page
Homogeneous compact geometries
We classify compact homogeneous geometries of irreducible spherical type and
rank at least 2 which admit a transitive action of a compact connected group,
up to equivariant 2-coverings. We apply our classification to polar actions on
compact symmetric spaces.Comment: To appear in: Transformation Group
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