Trieste, August 26-28 2014

K-homology and graph algebras

Finite summability and Cuntz-Krieger algebras, Part II: unbounded Fredholm modules

In this talk we will discuss how the finitely summable Fredholm modules discussed in Part I arise as bounded transforms of canonically defined unbounded representatives. The construction of these unbounded Fredholm modules exploits the dynamical picture of Cuntz-Krieger algebras as groupoid algebras of subshifts of finite type. Moreover, we show that all odd K-homology classes can be understood as localisations of a single bivariant cycle over the maximal abelian subalgebra. If time permits, more exotic Kasparov products with the above mentioned Belissard-Pearson spectral triples will be discussed. (Joint work with Magnus Goffeng).