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Journal of Noncommutative Geometry

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Volume 3, Issue 4, 2009, pp. 559–578
DOI: 10.4171/JNCG/46

Published online: 2009-12-23

The geometry of determinant line bundles in noncommutative geometry

Partha Sarathi Chakraborty and Varghese Mathai[1]

(1) University of Adelaide, Australia

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.

Keywords: Regularity, spectral triples, determinant line bundles, index theorem for families, connections, gauge transformations, dimension spectrum

Chakraborty Partha Sarathi, Mathai Varghese: The geometry of determinant line bundles in noncommutative geometry. J. Noncommut. Geom. 3 (2009), 559-578. doi: 10.4171/JNCG/46