Spectral triples for finitely presented groups, index 1.

Sébastien Palcoux (1)

1 IML - Institut de mathématiques de Luminy

Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index $1$.

Mots clés: non-commutative geometry; spectral triple; geometric group theory; Clifford algebra; Cayley graph; Dirac operator; finitely presented group

Domaines: Algèbres d'opérateurs [math.OA]

Sébastien Palcoux. Spectral triples for finitely presented groups, index 1.. 2010. ⟨hal-00537652v4⟩