Riemannian manifolds in noncommutative geometry
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Fecha
2012-07
Tipo
artículo original
Autores
Lord, Steven
Rennie, Adam
Várilly Boyle, Joseph C.
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Resumen
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.
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geometría no conmutativa, variedad riemanniana, triple espectral, grupo de Kasparov