CaltechAUTHORS
  A Caltech Library Service

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

[img] PDF - Submitted Version
See Usage Policy.

366Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170712-075152597

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:
URLURL TypeDescription
https://doi.org/10.1016/j.geomphys.2008.07.007DOIArticle
http://www.sciencedirect.com/science/article/pii/S0393044008001125PublisherArticle
https://arxiv.org/abs/0807.2924arXivDiscussion 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 AgencyGrant Number
NSFDMS-0651925
Subject Keywords:3-manifolds; Branched coverings; Correspondences; Cobordisms; Time evolution
Issue or Number:12
Classification Code:58B34; 57M12; 57C20; 82A15
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)
Usage Policy: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:03 Oct 2019 18:14

Repository Staff Only: item control page