Title

Curvature of differentiable Hilbert modules and Kasparov modules

Publication Name

Advances in Mathematics

Abstract

In this paper we introduce the curvature of densely defined universal connections on Hilbert C⁎-modules relative to a spectral triple (or unbounded Kasparov module), obtaining a well-defined curvature operator. Fixing the spectral triple, we find that modulo junk forms, the curvature only depends on the represented form of the universal connection. We refine our definition of curvature to factorizations of unbounded Kasparov modules. Our definition recovers all the curvature data of a Riemannian submersion of compact manifolds, viewed as a KK-factorization.

Open Access Status

This publication may be available as open access

Article Number

108128

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Link to publisher version (DOI)

http://dx.doi.org/10.1016/j.aim.2021.108128