File:Artin generators of the braid group.svg

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Original file(SVG file, nominally 477 × 253 pixels, file size: 37 KB)

Captions

Captions

Artin generators of the braid group

Summary[edit]

Description
English: The figure shows the Artin generators of the braid group and a braid word. The inputs of the braid strands are numbered.
Русский: Изображены образующие Артина группы кос и косовое слово, составленное из них. Начальные кончики нитей пронумерованы.
Date
Source Own work
Author MauveAccueil

LaTeX source[edit]

\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{braids}

\begin{document}
\begin{tikzpicture}[rotate=90,scale=0.8, every node/.style={scale=0.8}]
\draw[black,dashed] (0,0) grid ++(7,1);
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 6,
  braid/height = 1cm,
  name prefix=braid,
] at (1,-0.25) {braid={
s_3
}};
\node at (1,1+0.5) {$1$};
\node at (3,1+0.5) {$i$};
\node at (4,1+0.63) {$i+1$};
\node at (6,1+0.5) {$n$};
\node at (-0.5,0.5) {{\LARGE $\sigma_i$}};

\begin{scope}[shift={(0,-3)}]
\draw[black,dashed] (0,0) grid ++(7,1);
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 6,
  braid/height = 1cm,
  name prefix=braid,
] at (1,-0.25) {braid={
s_3^{-1}
}};
\node at (1,1+0.5) {$1$};
\node at (3,1+0.5) {$i$};
\node at (4,1+0.63) {$i+1$};
\node at (6,1+0.5) {$n$};
\node at (-0.5,0.4) {{\LARGE $\sigma_i^{-1}$}};

\begin{scope}[shift={(0,-3-5)}]
\draw[black,dashed] (0,0) grid ++(7,6);
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 6,
  braid/height = 1cm,
  name prefix=braid,
] at (1,-0.25) {braid={
s_5s_1^{-1}s_3s_3s_2s_5^{-1}
}};
\node at (1,6+0.5) {$1$};
\node at (2,6+0.5) {$2$};
\node at (3,6+0.5) {$3$};
\node at (4,6+0.5) {$4$};
\node at (5,6+0.5) {$5$};
\node at (6,6+0.5) {$6$};
\node at (-0.5,0.4+5) {{\LARGE $\sigma_5^{-1}$}};
\node at (-0.5-0.1,0.5+4) {{\LARGE $\sigma_2$}};
\node at (-0.5-0.1,0.5+3) {{\LARGE $\sigma_3$}};
\node at (-0.5-0.1,0.5+2) {{\LARGE $\sigma_3$}};
\node at (-0.5,0.4+1) {{\LARGE $\sigma_1^{-1}$}};
\node at (-0.5-0.1,0.5) {{\LARGE $\sigma_5$}};
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document}

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current16:06, 8 February 2023Thumbnail for version as of 16:06, 8 February 2023477 × 253 (37 KB)MauveAccueil (talk | contribs)Numbers enlarged
19:12, 6 February 2023Thumbnail for version as of 19:12, 6 February 2023405 × 253 (37 KB)MauveAccueil (talk | contribs)paths export fixed
18:07, 6 February 2023Thumbnail for version as of 18:07, 6 February 2023432 × 270 (20 KB)MauveAccueil (talk | contribs)Uploaded own work with UploadWizard

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