\documentclass[12pt]{article}
\usepackage{psfig}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amscd}
\usepackage{url}
\usepackage{verbatim} 
\usepackage{color}
\usepackage{epsfig}
\usepackage{stmaryrd}
%\usepackage{amsrefs}
\title{Billiards notation}
\author{W. Patrick Hooper}

\def\C{\mathbb{C}}% 
\def\N{\mathbb{N}}% 
\def\Q{\mathbb{Q}}% 
\def\R{\mathbb{R}}% 
\def\Z{\mathbb{Z}}% 

\newcommand{\addnotation}[2]{{#1}\>\parbox{4.5in}{#2}\\\vspace{1em}\\}%

\begin{document}
\maketitle
\begin{tabbing}
\hspace{1.5in}\=\\
\addnotation{$\gamma$}{a closed geodesic on the double of a triangle, ${\mathcal D}(T)$}
\addnotation{$\widehat{\gamma}$}{a periodic billiard path in a triangle}
\addnotation{$\Delta$}{the parameter space of marked triangles}
\addnotation{${\mathcal D}$, ${\mathcal D}(T)$}{double of a triangle $T$ across its edges (an Euclidean cone surface)}
\addnotation{$F$}{a defining function for an edge of $O(W)$ ($F=\textrm{Im}(\pm P \overline{Q})$)}
\addnotation{$H$, $H(W)$}{the {\em hexpath} (the path in the hexagonal grid corresponding to the combinatorial type $W$)}
\addnotation{$\textrm{MT}$,$\textrm{MT}(T)$}{the minimal translation surface corresponding to a triangle $T$}
\addnotation{$O$, $O(W)$}{an {\em orbit tile} corresponding to the word $W$ (ie. the collection of triangles with billiard paths of combinatorial type $W$)}
\addnotation{$P$}{part of defining function for and edge of $O(W)$ (a map $\Delta \to \C$)}
\addnotation{$Q$}{part of defining function for and edge of $O(W)$ (a map $\Delta \to \C$)}
\addnotation{$\hat{Q}$, $\hat{Q}(W)$}{the {\em square path}, which is related to $H(W)$}
\addnotation{$T$}{a triangle}
\addnotation{$U$, $U(W,T)$}{{\em unfolding} of triangle $T$ with respect to combinatorial type $W$}
\addnotation{$\textrm{UAC}$,$\textrm{UAC}(X)$}{the {\em universal abelian cover} of the space $X$ ($X$ defaults to the 3-punctured sphere)}
\addnotation{$V_n$}{the Veech triangle with angles $(\pi/2n,\pi/2n,(\pi-1)/n)$}
\addnotation{$W$}{a {\em combinatorial type} (ie. an infinite periodic word in the letters $\{1,2,3\}$, representing edges hit by a potential periodic billiard path)}

\end{tabbing}
\end{document}
