01090nas a2200133   4500008004100000245005800041210005800099260001300157520067800170653003000848100002200878700002000900856003600920       2013                        en  d00aNoncommutative circle bundles and new Dirac operators0 aNoncommutative circle bundles and new Dirac operators  bSpringer3 aWe study spectral triples over noncommutative principal U(1) bundles. Basing
on the classical situation and the abstract algebraic approach, we propose an
operatorial definition for a connection and compatibility between the
connection and the Dirac operator on the total space and on the base space of
the bundle. We analyze in details the example of the noncommutative three-torus
viewed as a U(1) bundle over the noncommutative two-torus and find all
connections compatible with an admissible Dirac operator. Conversely, we find a
family of new Dirac operators on the noncommutative tori, which arise from the
base-space Dirac operator and a suitable connection.10aQuantum principal bundles1 aDabrowski, Ludwik1 aSitarz, Andrzej  uhttp://hdl.handle.net/1963/7384