Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces

Abstract

We introduce the notion of weak commensurabilty of arithmetic subgroups and relate it to the length equivalence and isospectrality of locally symmetric spaces. We prove many strong consequences of weak commensurabilty and derive from these many interesting results about isolength and isospectral locally symmetric spaces.

62 pages

References in corpus (1)

• Bounded generation of SL(n,A) (after D. Carter, G. Keller and E. Paige)

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• Small isospectral and nonisometric orbifolds of dimension 2 and 3
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