Graphs, spectral triples and Dirac zeta functions
Operator Algebras
2009-04-09 v1 Differential Geometry
Dynamical Systems
Abstract
To a finite, connected, unoriented graph of Betti-number g>=2 and valencies >=3 we associate a finitely summable, commutative spectral triple (in the sense of Connes), whose induced zeta functions encode the graph. This gives another example where non-commutative geometry provides a rigid framework for classification.
Cite
@article{arxiv.0904.1291,
title = {Graphs, spectral triples and Dirac zeta functions},
author = {Jan Willem de Jong},
journal= {arXiv preprint arXiv:0904.1291},
year = {2009}
}
Comments
13 pages, 4 figures