Duke Mathematical Journal
- Duke Math. J.
- Volume 135, Number 2 (2006), 361-379.
Division algebras and noncommensurable isospectral manifolds
A. W. Reid [R, Theorem 2.1] showed that if and are arithmetic lattices in or in which give rise to isospectral manifolds, then and are commensurable (after conjugation). We show that for and or for , the situation is quite different; there are arbitrarily large finite families of isospectral noncommensurable compact manifolds covered by . The constructions are based on the arithmetic groups obtained from division algebras with the same ramification points but different invariants
Duke Math. J., Volume 135, Number 2 (2006), 361-379.
First available in Project Euclid: 17 October 2006
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Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi. Division algebras and noncommensurable isospectral manifolds. Duke Math. J. 135 (2006), no. 2, 361--379. doi:10.1215/S0012-7094-06-13525-1. https://projecteuclid.org/euclid.dmj/1161093268