Riemannian manifolds in noncommutative geometry

Steven Lord, Adam Rennie*, Joseph C. Várilly

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    29 Citations (Scopus)

    Abstract

    We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin. c manifolds; and conversely, in the presence of a spin. c structure. We also show how to obtain an analogue of Kasparov's fundamental class for a Riemannian manifold, and the associated notion of Poincaré duality. Along the way we clarify the bimodule and first-order conditions for spectral triples.

    Original languageEnglish
    Pages (from-to)1611-1638
    Number of pages28
    JournalJournal of Geometry and Physics
    Volume62
    Issue number7
    DOIs
    Publication statusPublished - Jul 2012

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