NCG seminar at SISSA (1 December)

[Emanuele Tuillier Illingworth]

NONCOMMUTATIVE GEOMETRY SEMINAR

B. Mesland (University of Warwick)

"Noncommutative geometry on Cuntz-Krieger algebras"

Monday 1 Dec. 16:00, SISSA room 134

We produce a variety of odd bounded Fredholm modules and odd spectral 
triples on Cuntz-Krieger algebras by means of realizing these algebras 
as ``the algebra of functions on a non-commutative space" coming from a 
sub shift of finite type. We show that any odd $K$-homology class can be 
represented by such an odd bounded Fredholm module or odd spectral 
triple. The odd bounded Fredholm modules that are constructed are 
finitely summable. The spectral triples are $\theta$-summable, although 
their phases will already on the level of analytic $K$-cycles be 
finitely summable bounded Fredholm modules. Using the unbounded Kasparov 
product, we exhibit a family of generalized spectral triples, related to 
work of Bellissard-Pearson, possessing mildly unbounded commutators, 
whilst still giving well defined $K$-homology classes.