Coverings, correspondences, and noncommutative geometry

Marcolli, Matilde and Zainy al-Yasry, Ahmad (2008) Coverings, correspondences, and noncommutative geometry. Journal of Geometry and Physics, 58 (12). pp. 1639-1661. ISSN 0393-0440. doi:10.1016/j.geomphys.2008.07.007. https://resolver.caltech.edu/CaltechAUTHORS:20170712-075152597

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Abstract

We construct an additive category where objects are embedded graphs in the 3-sphere and morphisms are 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.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1016/j.geomphys.2008.07.007	DOI	Article
http://www.sciencedirect.com/science/article/pii/S0393044008001125	Publisher	Article
https://arxiv.org/abs/0807.2924	arXiv	Discussion Paper

Additional Information:

© 2008 Elsevier B.V. Received 7 January 2008. Received in revised form 15 June 2008. Accepted 12 July 2008. Available online 20 July 2008. We thank the referee for many very useful comments and suggestions. The first author is partially supported by NSF-grant DMS-0651925.

Funders:

Funding Agency	Grant Number
NSF	DMS-0651925

Subject Keywords:

3-manifolds; Branched coverings; Correspondences; Cobordisms; Time evolution

Issue or Number:

Classification Code:

58B34; 57M12; 57C20; 82A15

DOI:

10.1016/j.geomphys.2008.07.007

Record Number:

CaltechAUTHORS:20170712-075152597

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20170712-075152597

Official Citation:

Matilde Marcolli, Ahmad Zainy al-Yasry, Coverings, correspondences, and noncommutative geometry, Journal of Geometry and Physics, Volume 58, Issue 12, December 2008, Pages 1639-1661, ISSN 0393-0440, https://doi.org/10.1016/j.geomphys.2008.07.007. (http://www.sciencedirect.com/science/article/pii/S0393044008001125)

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No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

78982

Collection:

CaltechAUTHORS

Deposited By:

Ruth Sustaita

Deposited On:

12 Jul 2017 17:25

Last Modified:

15 Nov 2021 17:44

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