File:Braid-modular-group-cover.svg
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 376 × 153 pixels. Other resolutions: 320 × 130 pixels | 640 × 260 pixels | 1,024 × 417 pixels | 1,280 × 521 pixels | 2,560 × 1,042 pixels.
Original file (SVG file, nominally 376 × 153 pixels, file size: 27 KB)
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. |
||
| 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. |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:19, 7 May 2009 | | 376 × 153 (27 KB) | wikimediacommons>Nbarth | Fix conversion typo – add overline. |
File usage
The following 2 pages use this file:
