File:Braid-modular-group-cover.svg
Summary
| Description |
English: Commutative diagram showing the braid group B3 as the universal central extension of the modular group, sitting as lattices inside SL2(R) and its universal cover. |
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| Date | |||
| Source | Own work, created as per: en:meta:Help:Displaying a formula#Commutative diagrams; source code below. | ||
| Author | Nils R. Barth | ||
| Permission (Reusing this file) |
Nils R. Barth, the copyright holder of this work, hereby publishes it under the following license:
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LaTeX source
\documentclass{amsart}
\usepackage[all, ps, dvips]{xy} % Loading the XY-Pic package
% Using postscript driver for smoother
% curves
\usepackage{color} % For invisible frame
\DeclareMathOperator{\SL}{SL}
\DeclareMathOperator{\PSL}{PSL}
\begin{document}
\thispagestyle{empty} % No page numbers
\SelectTips{eu}{} % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt} % Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin
\xymatrix@R=6pt{
& B_3 \ar@{->>}[r] \ar@{^(->}[dd]
& \PSL_2(\mathbf{Z}) \ar@{^(->}[dd]\\
\mathbf{Z} \ar@{_(->}@/^/[ur] \ar@{^(->}@/_/[dr] \\
& \overline{\SL_2(\mathbf{R})} \ar@{->>}[r]
& \PSL_2(\mathbf{R})
}
$$}}} % end math, end frame
\end{document}
Licensing
 |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |