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

Abstract
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.

Author information

Department of Mathematics, 6188 Kemeny Hall, Dartmouth College, Hanover, NH 03755, USA
Benjamin.D.Linowitz@dartmouth.edu