Braid-modular-group-cover.svg
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Summary
| Description |
English:
Commutative diagram
showing the
braid group
B
3
as the universal central extension of the
modular group
, sitting as lattices inside
SL
2
(
R
)
and its universal cover.
|
||
| 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:
|
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. |