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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Piecewise $ {\rm SL}\sb 2{\bf Z}$ geometry


Author: Peter Greenberg
Journal: Trans. Amer. Math. Soc. 335 (1993), 705-720
MSC: Primary 52B20
MathSciNet review: 1140914
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Abstract: Piecewise $ {\text{SL}}_2{\mathbf{Z}}$ geometry studies properties of the plane invariant under $ {\text{pl}}$-homeomorphisms which, locally, have the form $ x \mapsto Ax + b$ , with $ A \in {\text{SL}}_2{\mathbf{Z}}$, $ b \in {{\mathbf{Q}}^2}$ , and whose singular lines are rational. In this paper, invariants of polygons are obtained, relations with Pick's theorem are described, and a conjecture is posed.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1140914-1
Keywords: Piecewise linear homeomorphisms
Article copyright: © Copyright 1993 American Mathematical Society