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| {{Unreferenced|date=December 2009}}
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| This is a [[glossary]] of terms specific to [[differential geometry]] and [[differential topology]].
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| The following two glossaries are closely related:
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| *[[Glossary of general topology]]
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| *[[Glossary of Riemannian and metric geometry]].
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| See also:
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| *[[List of differential geometry topics]]
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| Words in ''italics'' denote a self-reference to this glossary.
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| {{compactTOC8|side=yes|top=yes|num=yes}}
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| __NOTOC__
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| ==A==
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| '''[[Atlas (topology)|Atlas]]'''
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| ==B==
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| '''Bundle''', see ''fiber bundle''.
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| ==C==
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| '''[[Chart (topology)|Chart]]'''
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| '''[[Cobordism]]'''
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| '''[[Codimension]]'''. The codimension of a submanifold is the dimension of the ambient space minus the dimension of the submanifold.
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| '''[[Connected sum]]'''
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| '''[[Connection (mathematics)|Connection]]'''
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| '''[[Cotangent bundle]]''', the vector bundle of cotangent spaces on a manifold.
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| '''[[Cotangent space]]''' | |
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| ==D==
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| '''[[Diffeomorphism]].''' Given two [[Manifold#Differentiable_manifolds|differentiable manifolds]]
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| ''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.
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| '''Doubling,''' given a manifold ''M'' with boundary, doubling is taking two copies of ''M'' and identifying their boundaries.
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| As the result we get a manifold without boundary.
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| ==E==
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| '''[[Embedding]]'''
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| ==F==
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| '''Fiber'''. In a fiber bundle, π: ''E'' → ''B'' the [[preimage]] π<sup>−1</sup>(''x'') of a point ''x'' in the base ''B'' is called the fiber over ''x'', often denoted ''E''<sub>''x''</sub>.
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| '''[[Fiber bundle]]'''
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| '''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.
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| '''[[Frame bundle]]''', the principal bundle of frames on a smooth manifold.
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| '''[[Flow (mathematics)|Flow]]'''
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| ==G== | |
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| '''[[Genus (mathematics)|Genus]]'''
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| ==H==
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| '''Hypersurface'''. A hypersurface is a submanifold of ''codimension'' one.
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| ==I==
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| '''[[Embedding|Immersion]]'''
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| ==L==
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| '''[[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>]].
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| ==M==
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| '''[[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.
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| ==N==
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| '''[[Neat submanifold]]'''. A submanifold whose boundary equals its intersection with the boundary of the manifold into which it is embedded.
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| ==P==
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| '''[[Parallelizable]]'''. A smooth manifold is parallelizable if it admits a smooth global frame. This is equivalent to the tangent bundle being trivial.
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| '''[[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.
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| '''[[Pullback]]'''
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| ==S==
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| '''[[Section (fiber bundle)|Section]]'''
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| '''[[Submanifold]]''', the image of a smooth embedding of a manifold.
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| '''[[Submersion (mathematics)|Submersion]]'''
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| '''[[Surface]]''', a two-dimensional manifold or submanifold.
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| '''[[systolic geometry|Systole]]''', least length of a noncontractible loop.
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| ==T==
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| '''[[Tangent bundle]]''', the vector bundle of tangent spaces on a differentiable manifold.
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| '''Tangent field''', a ''section'' of the tangent bundle. Also called a ''vector field''.
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| '''[[Tangent space]]'''
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| '''[[Torus]]'''
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| '''[[Transversality (mathematics)|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.
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| '''Trivialization'''
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| ==V==
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| '''[[Vector bundle]]''', a fiber bundle whose fibers are vector spaces and whose transition functions are linear maps.
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| '''[[Vector field]]''', a section of a vector bundle. More specifically, a vector field can mean a section of the tangent bundle.
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| ==W==
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| '''[[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'' ×''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.
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| {{DEFAULTSORT:Glossary Of Differential Geometry And Topology}}
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| [[Category:Glossaries of mathematics|Geometry]]
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| [[Category:Differential geometry| ]]
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| [[Category:Differential topology| ]]
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An author is known through name of Gabrielle Lattimer though she doesn't tremendously like being called in this way. To bake is something that she actually is been doing for months and months. Her job was a cashier but very quickly her husband and your spouse will start their own family based business. She's always loved living South Carolina. She is running and maintaining a blog here: http://prometeu.net
Check out my weblog clash of clans hack cydia (just click the up coming site)