\documentclass{amsart}
\usepackage[all, ps]{xy} % Loading the XY-Pic package
                         % Using postscript driver for smoother curves
\usepackage{color}       % For invisible frame
\begin{document}
\thispagestyle{empty} % No page numbers
\SelectTips{eu}{}     % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt} % Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin
 
\xymatrix@=6pt{
&\{\pm 1\}
  \ar@{^(->}@/_1pc/[ddl]
  \ar@{_(->}@/^1pc/[ddr]
\\ \\
   2 \cdot A_n      \ar@{->>}[dd] \ar@{^(->}[rr]
 &&2 \cdot S_n^\pm  \ar@{->>}[dd] \ar@{->>}@/^1pc/[rrd]
\\
 &&
&&\{\pm 1\}
\\
   A_n              \ar@{^(->}[rr]
 &&S_n
\ar@{->>}@/_1pc/[rru]^{\operatorname{sgn}}
}
 
$$}}} % end math, end frame
\end{document}