A spectral triple for noncommutative compact surfaces
Volume 120 / 2020
Banach Center Publications 120 (2020), 121-134
MSC: 58B34, 46L87.
DOI: 10.4064/bc120-9
Abstract
A Dirac operator is presented that will yield a $1^+$-summable regular even spectral triple for all noncommutative compact surfaces defined as subalgebras of the Toeplitz algebra. Connes’ conditions for noncommutative spin geometries are analyzed and it is argued that the failure of some requirements is mainly due to a wrong choice of a noncommutative spin bundle.
