New York Journal of Mathematics
Volume 18 (2012) 451-461


Benjamin Linowitz

Isospectral towers of Riemannian manifolds

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Published: June 14, 2012
Keywords: Isospectral tower, quaternion order, Sunada's method
Subject: Primary 58J53; Secondary 11F06

In this paper we construct, for n≧ 2, arbitrarily large families of infinite towers of compact, orientable Riemannian n-manifolds which are isospectral but not isometric at each stage. In dimensions two and three, the towers produced consist of hyperbolic 2-manifolds and hyperbolic 3-manifolds, and in these cases we show that the isospectral towers do not arise from Sunada's method.

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Department of Mathematics, 6188 Kemeny Hall, Dartmouth College, Hanover, NH 03755, USA