Graphs, spectral triples and Dirac zeta functions

Details Graphs, spectral triples and Dirac zeta functions Graphs, spectral triples and Dirac zeta functions

2009-04-08

arxiv.org/abs/0904.1291v1

Mathematics

Operator Algebras

13 pages, 4 figures

Scientific paper

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.

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