File:Braid-modular-group-cover.svg

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Original file ‎(SVG file, nominally 376 × 153 pixels, file size: 27 KB)

Captions

Captions

Add a one-line explanation of what this file represents

Summary[edit]

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:
Public domain 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.

LaTeX source[edit]

\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[edit]

Public domain 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/TimeThumbnailDimensionsUserComment
current16:19, 7 May 2009Thumbnail for version as of 16:19, 7 May 2009376 × 153 (27 KB)Nbarth (talk | contribs)Fix conversion typo – add overline.
16:10, 7 May 2009Thumbnail for version as of 16:10, 7 May 2009376 × 153 (27 KB)Nbarth (talk | contribs){{Information |Description = {{en|Commutative diagram showing the braid group ''B''<sub>3</sub> as the universal central extension of the modular group, sitting as lattices inside [[:en

You cannot overwrite this file.

There are no pages that use this file.

File usage on other wikis

The following other wikis use this file:

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Braid-modular-group-cover.svg&oldid=831444125"