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{{Unreferenced|date=December 2009}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
This is a [[glossary]] of terms specific to [[differential geometry]] and [[differential topology]].
The following two glossaries are closely related:
*[[Glossary of general topology]]
*[[Glossary of Riemannian and metric geometry]].


See also:
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
*[[List of differential geometry topics]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


Words in ''italics'' denote a self-reference to this glossary.
Registered users will be able to choose between the following three rendering modes:


{{compactTOC8|side=yes|top=yes|num=yes}}
'''MathML'''
__NOTOC__
:<math forcemathmode="mathml">E=mc^2</math>


==A==
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


'''[[Atlas (topology)|Atlas]]'''
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


==B==
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


'''Bundle''', see ''fiber bundle''.
==Demos==


==C==
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


'''[[Chart (topology)|Chart]]'''


'''[[Cobordism]]'''
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


'''[[Codimension]]'''. The codimension of a submanifold is the dimension of the ambient space minus the dimension of the submanifold.
==Test pages ==


'''[[Connected sum]]'''
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


'''[[Connection (mathematics)|Connection]]'''
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
'''[[Cotangent bundle]]''', the vector bundle of cotangent spaces on a manifold.
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
'''[[Cotangent space]]'''
 
==D==
 
'''[[Diffeomorphism]].''' Given two [[Manifold#Differentiable_manifolds|differentiable manifolds]]
''M'' and ''N'', a [[bijective map]] <math>f</math> from ''M'' to ''N'' is called a '''diffeomorphism''' if both <math>f:M\to N</math> and its inverse <math>f^{-1}:N\to M</math> are [[smooth function]]s.
 
'''Doubling,''' given a manifold ''M'' with boundary, doubling is taking two copies  of ''M'' and identifying their boundaries.  
As the result we get a manifold without boundary.
 
==E==
 
'''[[Embedding]]'''
 
==F==
 
'''Fiber'''. In a fiber bundle, π: ''E'' → ''B'' the [[preimage]] π<sup>&minus;1</sup>(''x'') of a point ''x'' in the base ''B'' is called the fiber over ''x'', often denoted ''E''<sub>''x''</sub>.
 
'''[[Fiber bundle]]'''
 
'''Frame'''.  A '''frame''' at a point of a [[differentiable manifold]] ''M'' is a [[basis of a vector space|basis]] of the [[tangent space]] at the point. 
 
'''[[Frame bundle]]''', the principal bundle of frames on a smooth manifold.
 
'''[[Flow (mathematics)|Flow]]'''
 
==G==
 
'''[[Genus (mathematics)|Genus]]'''
 
==H==
 
'''Hypersurface'''. A hypersurface is a submanifold of ''codimension'' one.
 
==I==
 
'''[[Embedding|Immersion]]'''
 
==L==
 
'''[[Lens space]]'''. A lens space is a quotient of the [[3-sphere]] (or (2''n'' + 1)-sphere) by a free isometric [[group action|action]] of [[cyclic group|'''Z'''<sub>k</sub>]].
 
==M==
 
'''[[Manifold]]'''. A topological manifold is a locally Euclidean [[Hausdorff space]]. (In Wikipedia, a manifold need not be [[paracompact]] or [[second-countable space|second-countable]].) A ''C<sup>k</sup>'' manifold is a differentiable manifold whose chart overlap functions are ''k'' times continuously differentiable. A ''C''<sup>∞</sup> or smooth manifold is a differentiable manifold whose chart overlap functions are infinitely continuously differentiable.
 
==P==
 
'''[[Parallelizable]]'''. A smooth manifold is parallelizable if it admits a smooth global frame. This is equivalent to the tangent bundle being trivial.
 
'''[[Principal bundle]]'''. A principal bundle is a fiber bundle ''P'' → ''B'' together with an [[group action|action]] on ''P'' by a [[Lie group]] ''G'' that preserves the fibers of ''P'' and acts simply transitively on those  fibers.
 
'''[[Pullback]]'''
 
==S==
 
'''[[Section (fiber bundle)|Section]]'''
 
'''Submanifold'''. A submanifold is the image of a smooth embedding of a manifold.
 
'''[[Submersion (mathematics)|Submersion]]'''
 
'''[[Surface]]''', a two-dimensional manifold or submanifold.
 
'''[[systolic geometry|Systole]]''', least length of a noncontractible loop.
 
==T==
 
'''[[Tangent bundle]]''', the vector bundle of tangent spaces on a differentiable manifold.
 
'''Tangent field''', a ''section'' of the tangent bundle. Also called a ''vector field''.
 
'''[[Tangent space]]'''
 
'''[[Torus]]'''
 
'''Transversality'''. Two submanifolds ''M'' and ''N'' intersect transversally if at each point of intersection ''p'' their tangent spaces <math>T_p(M)</math> and <math>T_p(N)</math> generate the whole tangent space at ''p'' of the total manifold.
 
'''Trivialization'''
 
==V==
 
'''[[Vector bundle]]''', a fiber bundle whose fibers are vector spaces and whose transition functions are linear maps.
 
'''[[Vector field]]''', a section of a vector bundle. More specifically, a vector field can mean a section of the tangent bundle.
 
==W==
 
'''[[Whitney sum]]'''. A Whitney sum is an analog of the direct product for vector bundles. Given two vector bundles α and β over the same base ''B'' their [[cartesian product]] is a vector bundle over ''B'' &times;''B''. The diagonal map <math>B\to B\times B</math> induces a vector bundle over ''B'' called the Whitney sum of these vector bundles and denoted by α⊕β.
 
{{DEFAULTSORT:Glossary Of Differential Geometry And Topology}}
[[Category:Glossaries of mathematics|Geometry]]
[[Category:Differential geometry| ]]
[[Category:Differential topology| ]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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