Hyperbolic jigsaws and families of pseudomodular groups I

Abstract

We show that there are infinitely many commensurability classes of pseudomodular groups, thus answering a question raised by Long and Reid. These are Fuchsian groups whose cusp set is all of the rationals but which are not commensurable to the modular group. We do this by introducing a general construction for the fundamental domains of Fuchsian groups obtained by gluing together marked ideal triangular tiles, which we call hyperbolic jigsaw groups.

arXiv comment21 pages, 4 figures, comments welcomed. Section 8 rewritten with a stronger result. Minor corrections to other parts. Grant acknowledgement added

Cited by in corpus (1)

• New Examples from the Jigsaw Groups Construction