Riemannian manifolds in noncommutative geometry

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Lord, Steven²  Rennie, Adam¹  Varilly, Joseph C.³ 

[1] Australian Natl Univ, Inst Math Sci, Canberra, ACT 0200, Australia

[2] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

[3] Univ Costa Rica, Escuela Matemat, San Jose 2060, Costa Rica

关键词: Noncommutative geometry;    Spectral triple;    Kasparov product;   

DOI  :  10.1016/j.geomphys.2012.03.004

来源: Elsevier

【 摘 要 】

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 Poincare duality. Along the way we clarify the bimodule and first-order conditions for spectral triples. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free