arXiv subjects

Jan Jitse Venselaar

Publications and source records attributed to Jan Jitse Venselaar.

3 recordsLinked to original sources

arXiv2015

The geometry of quantum lens spaces: real spectral triples and bundle structure

We study almost real spectral triples on quantum lens spaces, as orbit spaces of free actions of cyclic groups on the spectral geometry on the quantum group $SU_q(2)$. These spectral triples are given by weakening some of the conditions of a real spectral triple. We classify the irreducible almost real spectral triples on quantum lens spaces and we study unitary equivalences of such quantum lens spaces. Applying a useful characterization of principal $U(1)$-fibrations in noncommutative geometry, we show that all such quantum lens spaces are principal $U(1)$-fibrations over quantum teardrops.

math.QA↗

arXiv2012

Morita "equivalences" of equivariant torus spectral triples

In general, Morita equivalence of spectral triples need not be a symmetric relation. In this paper, we show that Morita equivalence of spectral triples is an equivalence relation for equivariant torus spectral triples.

math.OA↗

arXiv2011

Classification of spin structures on the noncommutative n-torus

We classify spin structures on the noncommutative torus, and find that the noncommutative n-torus has 2^n spin structures, corresponding to isospectral deformations of spin structures on the commutative n-torus. For n>3 the classification depends on Connes' spin manifold theorem. In addition, we study unitary equivalences of these spin structures.

math.OA↗