Riemannian manifolds in noncommutative geometry
نویسندگان
چکیده
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. Disciplines Engineering | Science and Technology Studies Publication Details Lord, S., Rennie, A. & Varilly, J. C. (2012). Riemannian manifolds in noncommutative geometry. Journal of Geometry and Physics, 62 (7), 1611-1638. This journal article is available at Research Online: http://ro.uow.edu.au/eispapers/478 Riemannian Manifolds in Noncommutative Geometry Steven Lord School of Mathematical Sciences, University of Adelaide Adelaide 5005, South Australia, Australia Adam Rennie Mathematical Sciences Institute, Australian National University Acton 0200, Canberra, Australia Joseph C. Várilly Escuela de Matemática, Universidad de Costa Rica,San José 2060, Costa Rica
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