Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

Piecewise $\textrm {SL}_ 2\textbf {Z}$ geometry


Author: Peter Greenberg
Journal: Trans. Amer. Math. Soc. 335 (1993), 705-720
MSC: Primary 52B20
DOI: https://doi.org/10.1090/S0002-9947-1993-1140914-1
MathSciNet review: 1140914
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 52B20

Retrieve articles in all journals with MSC: 52B20


Additional Information

Keywords: Piecewise linear homeomorphisms
Article copyright: © Copyright 1993 American Mathematical Society