Cornelissen, Gunther and Marcolli, Matilde (2008) Zeta functions that hear the shape of a Riemann surface. Journal of Geometry and Physics, 58 (5). pp. 619-632. ISSN 0393-0440. https://resolver.caltech.edu/CaltechAUTHORS:CORjgp08
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Abstract
To a compact hyperbolic Riemann surface, we associate a finitely summable spectral triple whose underlying topological space is the limit set of a corresponding Schottky group, and whose "Riemannian" aspect (Hilbert space and Dirac operator) encode the boundary action through its Patterson-Sullivan measured. We prove that the ergodic rigidity theorem for this boundary action implies that the zeta functions of the spectral triple suffice to characterize the (anti-)complex isomorphism class of the corresponding Riemann surface. Thus, you can hear the complex analytic shape of a Riemann surface, by listening to a suitable spectral triple.
Item Type: | Article | ||||||||||||
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Additional Information: | © 2008 Elsevier Ltd. Received 9 November 2007; revised 17 December 2007; accepted 30 December 2007. Available online 6 January 2008. | ||||||||||||
Subject Keywords: | non-commutative geometry; spectral triples; Kleinian-groups; manifolds; algebras; rigidity; curves; set | ||||||||||||
Issue or Number: | 5 | ||||||||||||
Classification Code: | MSC: 20H10; 57S30; 58B34 | ||||||||||||
Record Number: | CaltechAUTHORS:CORjgp08 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:CORjgp08 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 13544 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 08 May 2009 15:55 | ||||||||||||
Last Modified: | 03 Oct 2019 00:40 |
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