Graphs, spectral triples and Dirac zeta functions

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.

13 pages, 4 figures

References in corpus (2)

• Spectral triples for AF C*-algebras and metrics on the Cantor set
• Zeta functions that hear the shape of a Riemann surface