File:Spin-Pin-SO-O-definite.svg

\documentclass{amsart}
\usepackage[all, ps, dvips]{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]
\\ \\
   \operatorname{Spin}(n)     \ar@{->>}[dd] \ar@{^(->}[rr]
 &&\operatorname{Pin}_\pm(n)  \ar@{->>}[dd] \ar@{->>}@/^1pc/[rrd]^{D}
\\
 &&                                                             &&\{\pm 1\}
\\
   \operatorname{SO}(n)                     \ar@{^(->}[rr]
 &&\operatorname{O}(n)                      \ar@{->>}@/_1pc/[rru]^{\det}
}
 
$$}}} % end math, end frame
\end{document}