2017/10/31 by Buyalo, Sergei
#FOS: Mathematics #Metric Geometry (math.MG) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1710.11333
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 non-commutative geometry. A set of axioms charaterising spectral geometries is given. Bounded deformations of spectral geometries are studied and the relationship between the dimension of a spectral geometry and more traditional dimensions of metric spaces is investigated.