Number theoretic techniques in the theory of Lie groups and differential geometry

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The purpose of this article is to present a survey of our recent results on length commensurable and isospectral locally symmetric spaces. The geometric questions led us to the notion of "weak commensurability" of two Zariski-dense subgroups in a semi-simple Lie group. We have shown that for arithmetic subgroups, weak commensurability has surprisingly strong consequences. Our proofs make use of p-adic techniques and results from algebraic and transcendental number theory.
This is a slightly revised version of a survey article published in the Proceedings of the International Congress of Chinese Mathematicians held in 2007

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Differential Geometry, Number Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/169100

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.2401
 http://arxiv.org/abs/0809.2401

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arXiv