Dror Bar-Natan: Odds, Ends, Unfinished:

The Symbol Font dbnsymb

Dror Bar-Natan

Date: This Edition: Mar. 2, 2020; Revision History: Section 7.

Department of Mathematics
University of Toronto
Toronto Ontario M5S 3G3



This is the user manual for the symbol font dbnsymb.

tex dvi pdf ps
Sizes 60Kb 20Kb 120Kb 756Kb
Full mirror of this directory (.tar.gz, 544Kb)


1 Introduction

Over the last few years I occasionaly needed new symbols for the papers I was writing: overcrossings ( $\overcrossing$), undercrossings ( $\undercrossing$), pentagons ($\pentagon$), whatever. I've always settled for partial and ad-hoc solutions -- drawing little LATEX figures, combining existing symbols, etc. But if the AMS can have its own symbol package (amssymb.sty), why can't I have one too, with symbols to my liking, which are placed and scaled just like TEX's own?

dbnsymb is an attempt to create this personal font. I plan to use it in my own papers and ship it with those when I ship them out, just like I ship macros and figures. I plan to continue adding symbols to it as needed (or as requested by others) and to continue improving the existing symbols in it.

This document documents dbnsymb, it's usage, and how it can be modified. If you also need wheels ( $\fourwheel$) or double points ( $\doublepoint$) or anything else that's in, feel free to use it yourself. Finally, if you need your own symbols too, you are welcome to download dbnsymb and use it as a basis for your own modifications. I will also be happy to add symbols to dbnsymb for you, provided they are likely to be of interest for me and/or others with similar research interests.

2 Usage

To use dbnsymb, you need to have the files dbnsymb.mf and dbnsymb.sty somewhere where LATEX would see them -- your current working directory or in any other place where LATEX looks. These files can be downloaded by clicking on their names right above.

This done, you should include the package dbnsymb.sty in your document, cross your fingers, and hope for the best.

3 Example

If all goes well and the files dbnsymb.mf and dbnsymb.sty really are in LATEX's sight, the following example file should produce the output that follows it:

Here's a famous formula:
\[ V(\doublepoint) := V(\overcrossing) - V(\undercrossing), \]
and here's another way of writing it, with the new symbols as 
\[ V(K^\doublepoint) := V(K^\overcrossing) - V(K^\undercrossing). \]

Here's a famous formula:

$\displaystyle V(\doublepoint) := V(\overcrossing) - V(\undercrossing), $

and here's another way of writing it, with the new symbols as superscripts:

$\displaystyle V(K^\doublepoint) := V(K^\overcrossing) - V(K^\undercrossing). $

A more extensive example is this manual page itself. The source files are available here.

4 The symbol table

Symbol LATEXcommand Usage example
$\text{\Huge$\doublepoint$}$ \doublepoint $V(\doublepoint)$
$\text{\Huge$\overcrossing$}$ \overcrossing $V(\overcrossing)$
$\text{\Huge$\undercrossing$}$ \undercrossing $V(\undercrossing)$
$\text{\Huge$\virtualcrossing$}$ \virtualcrossing Virtual crossings ( $\virtualcrossing$) are endemic to quantum algebra
$\text{\Huge$\semivirtualover$}$ \semivirtualover Semi-virtuals are differences: $\semivirtualover\leftrightarrow\overcrossing-\virtualcrossing$.
$\text{\Huge$\semivirtualunder$}$ \semivirtualunder $\doublepoint\leftrightarrow\semivirtualover-\semivirtualunder$.
$\text{\Huge$\slashoverback$}$ \slashoverback $\langle\slashoverback\rangle$
$\text{\Huge$\svslashoverback$}$ \svslashoverback $\svslashoverback=\slashoverback-\crossing$
$\text{\Huge$\backoverslash$}$ \backoverslash $\langle\backoverslash\rangle$
$\text{\Huge$\svbackoverslash$}$ \svbackoverslash $\svbackoverslash=\backoverslash-\crossing$
$\text{\Huge$\Associator$}$ \Associator $\Associator$ and $\slashoverback$ generate parenthesized tangles.
$\text{\Huge$\righttwist$}$ \righttwist `` $\righttwist$'' denotes a ribbon with a right-handed twist
$\text{\Huge$\lefttwist$}$ \lefttwist `` $\lefttwist$'' denotes a ribbon with a left-handed twist
$\text{\Huge$\MobiusSymbol$}$ \MobiusSymbol `` $\MobiusSymbol$'' denotes the trivially embedded Möbius band
$\text{\Huge$\crossing$}$ \crossing  
$\text{\Huge$\smoothing$}$ \smoothing $zC(\smoothing)$
$\text{\Huge$\upupsmoothing$}$ \upupsmoothing The Conway relation $C(\overcrossing)-C(\undercrossing) = zC(\upupsmoothing)$
$\text{\Huge$\hsmoothing$}$ \hsmoothing The $A_1$ relation: $\HGraph=2\hbar(\hsmoothing-\crossing)$
$\text{\Huge$\HSaddleSymbol$}$ \HSaddleSymbol The cobordism $\HSaddleSymbol:\smoothing\to\hsmoothing$
$\text{\Huge$\ISaddleSymbol$}$ \ISaddleSymbol The cobordism $\ISaddleSymbol:\hsmoothing\to\smoothing$
$\text{\Huge$\fourinwheel$}$ \fourinwheel The cobordism $\fourinwheel:\bigcirc\to\emptyset$
$\text{\Huge$\twowheel$}$ \twowheel $\displaystyle\Omega=1+\frac{\twowheel}{48}$
$\text{\Huge$\fourwheel$}$ \fourwheel The wheeled Kontsevich integral $Z^\fourwheel(K)$
$\text{\Huge$\pentagon$}$ \pentagon The $\pentagon_m$ equation
$\text{\Huge$\hexagon$}$ \hexagon The $\hexagon_\pm$ relations
$\text{\Huge$\tetrahedron$}$ \tetrahedron $\tetrahedron$ is $6j$
$\text{\Huge$\isolatedchord$}$ \isolatedchord The framing correction $e^{f\frac{\isolatedchord}{2}}$
$\text{\Huge$\righttrefoil$}$ \righttrefoil $J(\righttrefoil)=-t^4+t^3+t$
$\text{\Huge$\lefttrefoil$}$ \lefttrefoil $J(\lefttrefoil)=-t^{-4}+t^{-3}+t^{-1}$
$\text{\Huge$\OpenHopfUp$}$ \OpenHopfUp The open Hopf link $\OpenHopfUp_{\!\!x}^y$
$\text{\Huge$\OpenHopf$}$ \OpenHopf The undirected open Hopf link $\OpenHopf_{\!\!x}^y$
$\text{\Huge$\HopfLink$}$ \HopfLink $Z^\fourwheel(\HopfLink) =
\langle\Omega,\Omega\rangle\exp ^{x}\!\!\frown^{y}$
$\text{\Huge$\botright$}$ \botright $\sigma_yZ(\OpenHopfUp_{\!x}^y)
= \Omega_y\exp_\char93 (\botright_x^{\!\!y})$
$\text{\Huge$\SGraph$}$ \SGraph The STU relation: $\SGraph=\TGraph-\UGraph$
$\text{\Huge$\TGraph$}$ \TGraph $\TGraph=\SGraph+\UGraph$
$\text{\Huge$\UGraph$}$ \UGraph $\UGraph=\TGraph-\SGraph$
$\text{\Huge$\IGraph$}$ \IGraph The IHX relation: $\IGraph=\HGraph-\XGraph$
$\text{\Huge$\HGraph$}$ \HGraph $\HGraph=\IGraph+\XGraph$
$\text{\Huge$\XGraph$}$ \XGraph $\XGraph=\HGraph-\IGraph$
$\text{\Huge$\YGraph$}$ \YGraph The AS relation: $\YGraph+\TwistedY=0$
$\text{\Huge$\FlippedYGraph$}$ \FlippedYGraph The w-vertices: $\{\YGraph,\FlippedYGraph\}$
$\text{\Huge$\TwistedY$}$ \TwistedY $\TwistedY=-\YGraph$
$\text{\Huge$\ThetaGraph$}$ \ThetaGraph $Z(\ThetaGraph) = \nu^{1/2}\otimes\nu^{1/2}\otimes\nu^{1/2}$
$\text{\Huge$\dumbbell$}$ \dumbbell  
$\text{\Huge$\wiggle$}$ \wiggle $Z^{\text{naive}}(\wiggle) = \nu^{-1}$
$\text{\Huge$\stonehenge$}$ \stonehenge The Stonehenge pairing $\langle D,K\rangle_\stonehenge$
$\text{\Huge$\inup$}$ \inup \begin{displaymath}\begin{array}{c} X \ \inup \ x \end{array}\end{displaymath}
$\text{\Huge$\actsonleft$}$ \actsonleft $G$ acts on $X$ on the left: $G\actsonleft X$
$\text{\Huge$\actsonright$}$ \actsonright $G$ acts on $X$ on the right: $X\actsonright G$
$\text{\Huge$\isotopic$}$ \isotopic  
$\text{\Huge$\horizontalchord$}$ \horizontalchord $Z^u(\overcrossing)=\exp(\horizontalchord)\virtualcrossing$
$\text{\Huge$\rightarrowdiagram$}$ \rightarrowdiagram $Z^w(\overcrossing)=\exp(\rightarrowdiagram)\virtualcrossing$
$\text{\Huge$\leftarrowdiagram$}$ \leftarrowdiagram $Z^w(\undercrossing)=\exp(-\leftarrowdiagram)\virtualcrossing$
$\text{\Huge$\cappededge$}$ \cappededge ${\mathcal A}^w(\cappededge)$
$\text{\Huge$\upcap$}$ \upcap In ${\mathcal A}^w(\upcap)$, only wheels survive
$\text{\Huge$\downcap$}$ \downcap $\downcap(D)$ cups the bottoms of the strands of $D$
$\text{\Huge$\doubletree$}$ \doubletree The $\doubletree$ map is key to associators and $Z^w$.
$\text{\Huge$\uppertriang$}$ \uppertriang $\uppertriang\subset gl_n$ represents the upper triangular matrices.
$\text{\Huge$\lowertriang$}$ \lowertriang $\lowertriang\oplus\uppertriang=gl_n\oplus{\mathfrak{a}}_n$.
$\text{\Huge$\OU$}$ \OU $\OU$ means Over then Under.
$\text{\Huge$\CanadianFlag$}$ \CanadianFlag Canad$\overset{\CanadianFlag}{\text{a}}$: Canad $\overset{\CanadianFlag}{\text{a}}$
$\text{\Huge$\dbnframe$}$ \dbnframe \hbox to 0pt{$\slashoverback$}$\dbnframe$: $\text{\hbox to 0pt{$\slashoverback$}$\dbnframe$}$

5 Modifying dbnsymb

The symbols in dnsymb were all drawn using xfig, an X-windows drawing program, and then converted to metafont using fig2dev (a standard companion program to xfig) assisted by a simple perl script that I wrote.

To add new symbols or create your own symbol font, follow the following steps:

The script makefont has an additional optional parameter, -f2m_opts filename, that may contain symbol by symbol options for fig2dev. See the manual page for fig2dev and the options file dbnsymb.f2m-opts used for the creation of dbnsymb.

6 Acknowledgement

I wish to thank Dylan P. Thurston for his comments, suggestions and extra symbols. The base for the Canadian flag symbol $\smash{\raisebox{6pt}{\text{\Huge $\CanadianFlag$}}}$ came from the Xfig Flag Library.

7 Revision History

March 3, 2020
$\FlippedYGraph$ added.
September 29, 2019
$\upupsmoothing$ added.
April 1, 2017
$\OU$ added.
January 28, 2017
$\uppertriang$ and $\lowertriang$ added.
October 8, 2015
$\downcap$ added.
January 27, 2014
$\horizontalchord$ added.
August 12, 2013
Minor tweaking.
November 30, 2011
$\doubletree$ added.
May 29, 2010
$\upcap$ added.
September 25, 2009
$\svslashoverback$ and $\svbackoverslash$ added.
April 19, 2009
$\cappededge$ added.
November 28, 2008
$\actsonleft$ and $\actsonright$ added.
November 12, 2008
$\rightarrowdiagram$ and $\leftarrowdiagram$ added.
September 25, 2008
$\semivirtualover$ and $\semivirtualunder$ added.
August 22, 2008
$\virtualcrossing$ added.
October 29, 2003
Canad $\overset{\CanadianFlag}{\text{a}}$ added!
October 27, 2003
Move to Toronto, some new symbols.
November 11, 2001
Some new symbols.
October 21, 2001
Some new symbols.
March 22, 2001
Bigger sized symbols in Section 4 in the html version.
January 25, 2001
Some new symbols.
May 18, 2000
Some new symbols, sizes adjusted so that $\dbnframe\simeq\square$ ($\dbnframe\simeq\square$).
May 7, 2000
Minor modifications and some extra symbols added.
April 26, 2000
Minor modifications.
April 25, 2000
Added ``full mirror'' download option.
April 24, 2000
Added a few symbols and Sections 56 and 7 and made a few minor modifications.
March 19, 2000
First version posted.

About this document ...

The Symbol Font dbnsymb

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