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Riemannian manifolds in noncommutative geometry

Journal Article


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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 spinc manifolds; and conversely, in the presence of a

    spinc 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.

Authors


  •   Lord, Steven (external author)
  •   Rennie, Adam C.
  •   Varilly, Joseph C. (external author)

Publication Date


  • 2012

Citation


  • Lord, S., Rennie, A. & Varilly, J. C. (2012). Riemannian manifolds in noncommutative geometry. Journal of Geometry and Physics, 62 (7), 1611-1638.

Scopus Eid


  • 2-s2.0-84860382281

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1483&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/478

Has Global Citation Frequency


Number Of Pages


  • 27

Start Page


  • 1611

End Page


  • 1638

Volume


  • 62

Issue


  • 7

Place Of Publication


  • Netherlands

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 spinc manifolds; and conversely, in the presence of a

    spinc 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.

Authors


  •   Lord, Steven (external author)
  •   Rennie, Adam C.
  •   Varilly, Joseph C. (external author)

Publication Date


  • 2012

Citation


  • Lord, S., Rennie, A. & Varilly, J. C. (2012). Riemannian manifolds in noncommutative geometry. Journal of Geometry and Physics, 62 (7), 1611-1638.

Scopus Eid


  • 2-s2.0-84860382281

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1483&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/478

Has Global Citation Frequency


Number Of Pages


  • 27

Start Page


  • 1611

End Page


  • 1638

Volume


  • 62

Issue


  • 7

Place Of Publication


  • Netherlands