Manifold Atlas:TeX in the Atlas

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Introduction

The manifold Atlas runs wikitex: writing mathematics in the Atlas is very similar to TeXing in other contexts.

If you wish to simply get started by looking at existing code, you may visit the following pages and hit the Edit button or View source button at the top of the page (please be sure not to actually edit anything however):

LaTeX formulas

The <wikitex> environment lets you to insert inline LaTeX formulas using the familiar dollar signs: all atlas articles begin and end with the <wikitex> tags. For example

<wikitex>;
... there is a diffeomorphism $f \co M^n_a \cong M^n_b$ ...
</wikitex>

will appear as:

there is a diffeomorphism f \co M^n_a \cong M^n_b

Please read the style guide for Latex conventions in the Atlas and for command shortcuts.

Finally note that the normal <math> tags are disabled so that there is a unique method for math markup.

Displayed formulas

Displayed formulas can be obtained by double-dollars $$...$$. You can get tags at the right margin by the command \eqno{...} within a displayed formula. There is no automatic numbering available, so please number your formulas by hand, if necessary.

Multiline formulas can be obtained by the AMS-LaTeX environments “gathered”, “aligned” and “alignedat”. For example,

<wikitex>;
$$
  \begin{aligned}
    H^k(K(G,k);H) &\cong \Hom(H_k(K(G,k);H) \\
                  &\cong \Hom(G,H).
  \end{aligned}
$$
</wikitex>

yields

\displaystyle    \begin{aligned}     H^k(K(G,k);H) &\cong \Hom(H_k(K(G,k),H) \\                   &\cong \Hom(G,H).   \end{aligned}

Equations

Equations, that is numbered displayed formulas can be written using \backslashbegin{equation} \backslashlabel{eq:name} ... \backslashend{equation}.

Refreshing <wikitex> commands

Note that WikiTex only creates each graphic file once and then uses that fixed graphic.

If you find that a WikiTeX command is producing the wrong symbol, e.g. if you are using user-defined commands then you can have WikiTeX up-date its graphics files as follows:

  • Replace the relevant <wikitex>; command(s) by
    • <wikitex refresh>;

If you are using user-defined commands, then up-date with

  • <wikitex refresh include="TeXInclude:Page_name>;

Note that using <wikitex refresh>; slows the page down since the graphics are refreshed each time the page is loaded.

Once your WikiTeX commands are working as they should, please remove the refresh from you <wikitex refresh>; commands.

Theorems, proofs and such

The Atlas has two theorem-like environments:

  • {{beginthm|par1|par2}} ... {{endthm}},
  • {{beginrem|par1|par2}} ... {{endrem}}.

The first produces emphasised text suitable for theorems, propositions, lemmas etc.

The second produces standard text suitable for remarks.

Both environments have two parameters: the first parameter contains the name of the statement. The second parameter is optional and contains any additions to the heading. For example:

Conjecture 4.1 (Novikov). The higher signatures are homotopy invariants.

is generated by the code

{{beginthm|Conjecture|(Novikov)}}
The higher signatures are homotopy invariants.
{{endthm}}

There is also a single proof environment {{beginproof}} ... {{endproof}}. For example

Proof. The proof follows from ... .

\square

is generated by the code

{{beginproof}} 
The proof follows from ... .
{{endproof}}

Intra-article referencing

You can label Theorems, Lemmas etc and refer to them just as you would in tex. Here is an example:

{{beginthm|Conjecture|[Borel Conjecture]}} <label>con:Borel_Conjecture</label>
Every aspherical closed manifold is topologically rigid.
{{endthm}}
In particular the Borel Conjecture 5.1 implies ...

Produces the output:

Conjecture 5.1 [Borel Conjecture].

Every aspherical closed manifold is topologically rigid.

In particular the Borel Conjecture 5.1 implies ... .

Footnotes

You can insert footnotes into your article as follows:

  • write your footnote inside <ref> ... </ref>
  • add a section at the end of your page after the reference section by writing
    • ==Footnotes== <references/>

For example: <ref> Here is a footnote. </ref> produces this footnote [1].

Fonts

WikiTeX gives the following commands for various fonts in math-mode:

  • $ ... \text{ } ... $ for up-right text: e.g. ... \text{Bundle} ...
  • $ ... \mathcal{ } ... $ for caligraphic text: e.g. ... \mathcal{BUNDLE} ...
  • $ ... \mathscr{ } ... $ for script text: e.g. ... \mathscr{BUNDLE} ...
  • $ ... \frak{ } ... $ for gothic text: e.g. ... \frak{BUNDLE} ...

User-defined commands

For each separate page, it is possible to create your own user-defined commands with WikiTeX:

  • You need to create an auxiliary page called TeXInclude:Page_name and simply place your new commands there.
  • In the page you are writing you then need to change the wikitex commands as follows:
    • replace <wikitex> with <wikitex include="TeXInclude:Page_name">

For example, see TeXInclude:Super manifolds: an incomplete survey and Super manifolds: an incomplete survey.

If you wish to create a TeXInclude page for a page you are working on please:

  1. check to see if the page already exists by going to the TeXInclude index
  2. create your TeXInclude page in the box below, make sure you type TeXInclude:Page_name

Notes on user-defined commands

  • Please ensure that your own commands do not conflict with the existing globally defined commands.
  • You can read about Namespaces in mediawiki here.

Diagrams

The Atlas supports the diagram package Xy-pic. So making diagrams with xy-pic in the Atlas works just as it would in a usual TeX file: make sure you are in math-mode. Here are a couple examples from the Atlas:

Further information is available from:

Lists

Lists are easily produced.

  • Just use \ast for each item.
    • To creata a sub-list, use \ast \ast.
  • If you want to number the list you can use # .
  • For more information see lists in Wikipedia.

LaTeX style guide

  • Shortcuts for blackboard bold capital letters are available: for example type $\Cc,\Qq,\Rr$ for \Cc,\Qq,\Rr.
  • Expressions consisting of more than one letter should usually not be written: For example, $Diff(M)$ since this results in the cumbersome: Diff(M). A TeX-nically better way is $\mathop{\mathrm{Diff}}(M)$, which yields the elegant rendering \mathop{\mathrm{Diff}}(M). For your convenience, some manifold-related expressions are predefined in the <wikitex> environment, in addition to the standard operators like \sin, \exp etc. Feel free to request more commonly used operators and abbreviations.
code result meaning
\id \id identity map
\Sq \Sq Steenrod squares
\Homeo \Homeo group of homeomorphisms of a topoloical space
\Diff \Diff group of diffeomorphisms of a smooth manifold
\SDiff \SDiff diffeomorphisms under some constraint
\Hom \Hom homomorphisms of an algebraic structure
\End \End endomorphisms
\Aut \Aut automorphisms
\Inn \Inn inner automorphisms
\Out \Out outer automorphisms
\GL \GL general linear group
\SL \SL special linear group
\SO \SO special orthogonal group
\SU \SU special unitary group
\Spin \Spin Spin group
\RP \RP real projective space
\CP \CP complex projective space
\HP \HP quaternionic projective space
\Top \Top topological category
\PL \PL piecewise linear category
\Cat \Cat any category
\KS \KS Kirby-Siebenmann class

Footnotes

  1. Here is a footnote.
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