The geometry of determinant line bundles in noncommutative geometry

The Geometry of Determinant Line Bundles in Noncommutative Geometry

This paper is concerned with the study of the geometry of determinant line bundles associated to families of spectral triples parametrized by the moduli space of gauge equivalent classes of Hermitian connections on a Hermitian finite projective module. We illustrate our results with some examples that arise in noncommutative geometry. Introduction In the mid 1990s, Connes and Moscovici [4] form...

The geometry of determinant line bundles in noncommutative geometry

This article is concerned with the study of the geometry of determinant line bundles associated to families of spectral triples parametrized by the moduli space of gauge equivalence classes of Hermitian connections on a Hermitian finite projective module. We illustrate our results with some examples that arise in noncommutative geometry. Mathematics Subject Classification (2000). 58B34; 46L87, ...

Noncommutative geometry

Duality in Noncommutative Geometry

The structure of spacetime duality and discrete worldsheet symmetries of compactified string theory is examined within the framework of noncommutative geometry. The full noncommutative string spacetime is constructed using the Fröhlich-Gawȩdzki spectral triple which incorporates the vertex operator algebra of the string theory. The duality group appears naturally as a subgroup of the automorphi...

Noncommutative Geometry of Foliations

We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.