Coverings, correspondences, and noncommutative geometry

JOURNAL OF GEOMETRY AND PHYSICS

卷:58

Article

Marcolli, Matilde¹  al-Yasry, Ahmad Zainy^1,2 

[1] Max Planck Inst Math, D-5300 Bonn, Germany

[2] Univ Baghdad, Baghdad, Iraq

关键词: 3-manifolds;    Branched coverings;    Correspondences;    Cobordisms;    Time evolution;   

DOI  :  10.1016/j.geomphys.2008.07.007

来源: Elsevier

【 摘 要 】

We construct an additive category where objects are embedded graphs in the 3-sphere and morphisms ire geometric correspondences given by 3-manifolds realized in different ways as branched covers of the 3-sphere, up to branched cover cobordisms. We consider dynamical systems obtained from associated convolution algebras endowed with time evolutions defined in terms of the underlying geometries. We describe the relevance of our construction to the problem of spectral correspondences in noncommutative geometry. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free