\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 I\}
  \ar@{^(->}@/_1pc/[ddl]
  \ar@{_(->}@/^1pc/[ddr]
\\ \\
   \operatorname{SO}(2k) \ar@{->>}[dd] \ar@{^(->}[rr]
 &&\operatorname{O}(2k)  \ar@{->>}[dd] \ar@{->>}@/^1pc/[rrd]^{\det}
\\
 &&                                                             &&\{\pm 1\}
\\
   \operatorname{PSO}(2k)              \ar@{^(->}[rr]
 &&\operatorname{PO}(2k)               \ar@{->>}@/_1pc/[rru]^{\det}
}

$$}}} % end math, end frame
\end{document}