Petersburg Department of Steklov Institute of Mathematics

PREPRINT 19/1999

SPECTRAL GEOMETRIES ON A COMPACT METRIC SPACE

This preprint was accepted September , 1999
Contact: S. V. Buyalo

ABSTRACT:
The notion of a spectral geometry on a compact metric space
$X$
is introduced. This notion serves as a discrete approximation of
$X$
motivated by the notion of a spectral triple from noncommutative geometry. A
set of axioms characterizing spectral geometries is given. Bounded
deformations of spectral geometries are studied and relationship between the
dimension of a spectral geometry and more traditional dimensions of metric
spaces is investigated.