chitr:Braid-modular-group-cover.svg

mool faail(SVG faail, saadhaaranat: 376 × 153 peeksels, faailaka aakaar: 27 KB)

varnan[sampaadan]

jaankaari
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.
dinaank
srot Own work, created as per: en:meta:Help:Displaying a formula#Commutative diagrams; source code below.
lekhak Nils R. Barth
anumati
(is faail ki pun: upayog)
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[sampaadan]

\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}

laaisensing[sampaadan]

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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vartamaan 16:19, 7 May 2009 16:19, 7 मई 2009 के संस्करण का अंगूठाकार प्रारूप। 376 × 153 (27 KB) Nbarth Fix conversion typo – add overline.
16:10, 7 May 2009 16:10, 7 मई 2009 के संस्करण का अंगूठाकार प्रारूप। 376 × 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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