Manifold Atlas:TeX in the Atlas

1 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$$__TOC__ == LaTeX formulas == The <tt><nowiki><wikitex></nowiki></tt> environment lets you to insert inline LaTeX formulas using the familiar dollar signs: all atlas articles begin and end with the <tt><nowiki><wikitex></nowiki></tt> tags. For example <pre> <wikitex>; ... there is a diffeomorphism $f \co M^n_a \cong M^n_b$ ... </wikitex> </pre> will appear as: <wikitex><blockquote> there is a diffeomorphism $f \co M^n_a \cong M^n_b$ </blockquote></wikitex> Please read the [[#LaTeX style guide|style guide]] for Latex conventions in the atlas and command shortcuts. Finally note that the normal <tt><nowiki><math></nowiki></tt> tags are disabled so that there is a unique method for math markup. === Displayed formulas === Displayed formulas can be obtained by double-dollars <tt><nowiki>$$...$$</nowiki></tt>. You can get tags at the right margin by the command <tt>\eqno{...}</tt> within a displayed formula. There is no automatic numbering available, so please number your formulas by hand, if necessary. Multiline formulas can be obtained by the AMS-LaTeX environments “gathered”, “aligned” and “alignedat”. For example, <pre> <wikitex>; $$ \begin{aligned} H^k(K(G,k);H) &\cong \Hom(H_k(K(G,k);H) \ &\cong \Hom(G,H). \end{aligned} $$ </wikitex> </pre> yields <wikitex>; $$ \begin{aligned} H^k(K(G,k);H) &\cong \Hom(H_k(K(G,k),H) \ &\cong \Hom(G,H). \end{aligned} $$ </wikitex> == Theorems, proofs and such == <wikitex>; The Atlas has a single theorem-like environment <tt><nowiki>{{beginthm|par1|par2}}</nowiki></tt> and <tt><nowiki>{{endthm}}</nowiki></tt>. The first parameter contains the name of the statement. The second parameter is optional and contains any additions to the theorem heading. For example: {{beginthm|Conjecture|(Novikov)}} The higher signatures are homotopy invariants. {{endthm}} is generated by the code <pre><nowiki> {{beginthm|Conjecture|(Novikov)}} The higher signatures are homotopy invariants. {{endthm}} </nowiki></pre> There is also a single proof environment <tt><nowiki>{{beginproof}}</nowiki></tt> and <tt><nowiki>{{endproof}}</nowiki></tt>. For example {{beginproof}} The proof follows from ... . {{endproof}} is generated by the code <pre><nowiki> {{beginproof}} The proof follows from ... . {{endproof}} </nowiki></pre> </wikitex> == Intra-article referencing == You can label Theorems, Lemmas etc and refer to them just as you would in tex. Here is an example: <pre> {{beginthm|Conjecture|[Borel Conjecture]}} '''&#92;label{con:Borel_Conjecture}''' Every aspherical closed manifold is topologically rigid. {{endthm}} In particular the Borel Conjecture '''&#92;ref{con:Borel_Conjecture}''' implies ... </pre> Produces the output: {{beginthm|Conjecture|[Borel Conjecture]}} \label{con:Borel_Conjecture} Every aspherical closed manifold is topologically rigid. {{endthm}} In particular the Borel Conjecture \ref{con:Borel_Conjecture} implies ... . Note that the following text can also be used: * '''<nowiki><label>label_name</label> </nowiki>''' in place of '''&#92;label{label_name}''' * '''<nowiki><ref>label_name</ref></nowiki>''' in place of '''&#92;ref{label_name}''' == Diagrams == The Atlas supports the diagram package [http://www.tug.org/applications/Xy-pic/ 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: * [[Exotic spheres#Further discussion|a braid]], * [[B-Bordism#Introduction|a simple triangle]]. Further information is available from: * [http://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/ The CTAN directory], * [[Media:Xyguide.pdf|the xy-pic users guide]], * [[Media:Xyrefer.pdf|the xy-pic reference manual]]. == Lists == <wikitex>; Lists are easily produced. * Just use $ \ast $ for each item. ** To creata a sub-list, use $ \ast \ast $. * If you want to number the list you can use <nowiki> # </nowiki>. * For more information see [[Wikipedia:Help:List|lists in Wikipedia]]. </wikitex> == LaTeX style guide == * Shortcuts for blackboard bold capital letters are available: for example type <tt><nowiki>$\Cc,\Qq,\Rr$</nowiki></tt> for <tex>\Cc,\Qq,\Rr</tex>. * Expressions consisting of more than one letter should usually not be written: For example, <tt><nowiki>$Diff(M)$</nowiki></tt> since this results in the cumbersome: <tex>Diff(M)</tex>. A TeX-nically better way is <tt><nowiki>$\mathop{\mathrm{Diff}}(M)$</nowiki></tt>, which yields the elegant rendering <tex>\mathop{\mathrm{Diff}}(M)</tex>. For your convenience, some manifold-related expressions are predefined in the <tt><nowiki><wikitex></nowiki></tt> environment, in addition to the standard operators like <tt><nowiki>\sin</nowiki></tt>, <tt><nowiki>\exp</nowiki></tt> etc. Feel free to request more commonly used operators and abbreviations. {| border=1 |- ! code ! result ! meaning |- | <tt>\id</tt> | <tex>\id</tex> | identity map |- | <tt>\Sq</tt> | <tex>\Sq</tex> | Steenrod squares |- | <tt>\Homeo</tt> | <tex>\Homeo</tex> | group of homeomorphisms of a topoloical space |- | <tt>\Diff</tt> | <tex>\Diff</tex> | group of diffeomorphisms of a smooth manifold |- | <tt>\SDiff</tt> | <tex>\SDiff</tex> | diffeomorphisms under some constraint |- | <tt>\Hom</tt> | <tex>\Hom</tex> | homomorphisms of an algebraic structure |- | <tt>\End</tt> | <tex>\End</tex> | endomorphisms |- | <tt>\Aut</tt> | <tex>\Aut</tex> | automorphisms |- | <tt>\Inn</tt> | <tex>\Inn</tex> | inner automorphisms |- | <tt>\Out</tt> | <tex>\Out</tex> | outer automorphisms |- | <tt>\GL</tt> | <tex>\GL</tex> | general linear group |- | <tt>\SL</tt> | <tex>\SL</tex> | special linear group |- | <tt>\SO</tt> | <tex>\SO</tex> | special orthogonal group |- | <tt>\SU</tt> | <tex>\SU</tex> | special unitary group |- | <tt>\Spin</tt> | <tex>\Spin</tex> | Spin group |- | <tt>\RP</tt> | <tex>\RP</tex> | real projective space |- | <tt>\CP</tt> | <tex>\CP</tex> | complex projective space |- | <tt>\HP</tt> | <tex>\HP</tex> | quaternionic projective space |- | <tt>\Top</tt> | <tex>\Top</tex> | topological category |- | <tt>\PL</tt> | <tex>\PL</tex> | piecewise linear category |- | <tt>\Cat</tt> | <tex>\Cat</tex> | any category |- | <tt>\KS</tt> | <tex>\KS</tex> | Kirby-Siebenmann class |}f \co M^n_a \cong M^n_b$

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

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

1.1 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

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

2 Theorems, proofs and such

The Atlas has a single theorem-like environment {{beginthm|par1|par2}} and {{endthm}}. The first parameter contains the name of the statement. The second parameter is optional and contains any additions to the theorem heading. For example:

Conjecture 2.1 (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}} and {{endproof}}. For example

Proof. The proof follows from ... .

$\square$$\square$

is generated by the code

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

3 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}'''
Every aspherical closed manifold is topologically rigid.
{{endthm}}
In particular the Borel Conjecture '''\ref{con:Borel_Conjecture}''' implies ...

Produces the output:

Conjecture 3.1 [Borel Conjecture].

Every aspherical closed manifold is topologically rigid.

In particular the Borel Conjecture 3.1 implies ... .

Note that the following text can also be used:

• <label>label_name</label> in place of \label{label_name}
• </wikitex><ref>label_name</ref><wikitex>; in place of \ref{label_name}

4 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:

• a braid,
• a simple triangle.

Further information is available from:

• The CTAN directory,
• the xy-pic users guide,
• the xy-pic reference manual.

5 Lists

Lists are easily produced.

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

6 LaTeX style guide

• Shortcuts for blackboard bold capital letters are available: for example type $\Cc,\Qq,\Rr$ for $\Cc,\Qq,\Rr$$\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)$$Diff(M)$. A TeX-nically better way is $\mathop{\mathrm{Diff}}(M)$, which yields the elegant rendering $\mathop{\mathrm{Diff}}(M)$$\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	Tex syntax error $\id$	identity map
\Sq	$\Sq$$\Sq$	Steenrod squares
\Homeo	$\Homeo$$\Homeo$	group of homeomorphisms of a topoloical space
\Diff	$\Diff$$\Diff$	group of diffeomorphisms of a smooth manifold
\SDiff	$\SDiff$$\SDiff$	diffeomorphisms under some constraint
\Hom	$\Hom$$\Hom$	homomorphisms of an algebraic structure
\End	$\End$$\End$	endomorphisms
\Aut	$\Aut$$\Aut$	automorphisms
\Inn	$\Inn$$\Inn$	inner automorphisms
\Out	$\Out$$\Out$	outer automorphisms
\GL	$\GL$$\GL$	general linear group
\SL	$\SL$$\SL$	special linear group
\SO	$\SO$$\SO$	special orthogonal group
\SU	$\SU$$\SU$	special unitary group
\Spin	$\Spin$$\Spin$	Spin group
\RP	$\RP$$\RP$	real projective space
\CP	$\CP$$\CP$	complex projective space
\HP	$\HP$$\HP$	quaternionic projective space
\Top	$\Top$$\Top$	topological category
\PL	$\PL$$\PL$	piecewise linear category
\Cat	$\Cat$$\Cat$	any category
\KS	$\KS$$\KS$	Kirby-Siebenmann class