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File:Braid-modular-group-cover.svg

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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:
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

\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

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.

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inception

7 May 2009

media type

image/svg+xml

checksum

d3e2eac04b50c80d7a406042123673469e435fa0

determination method or standard: SHA-1

data size

27,584 byte

height

153 pixel

width

376 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current16:19, 7 May 2009Thumbnail for version as of 16:19, 7 May 2009376 × 153 (27 KB)NbarthFix conversion typo – add overline.
16:10, 7 May 2009Thumbnail for version as of 16:10, 7 May 2009376 × 153 (27 KB)Nbarth{{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

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