topics in manifold theory
A manifold^{} is a space that is locally like ${\mathbb{R}}^{n}$, however lacking a preferred system of coordinates. Furthermore, a manifold can have global topological properties, such as noncontractible loops (http://planetmath.org/Curve), that distinguish it from the topologically trivial ${\mathbb{R}}^{n}$.
By imposing different restrictions on the transition functions of a manifold, one obtain different types of manifolds:
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${C}^{k}$ manifolds, smooth manifolds

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real analytic manifold
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symplectic manifolds^{}, where transition functions are symplectomorphisms. On such manifolds, one can formulate the Hamilton equations.
Special types of manifolds
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On manifolds, one can introduce more . Some examples are:
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fiber bundles^{} and sheaves
Examples

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spacetime manifold in general relativity

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phase space in mechanics
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See also
For the formal definition click here (http://planetmath.org/Manifold)
http://en.wikipedia.org/wiki/ManifoldManifold entry at Wikipedia
Title  topics in manifold theory 

Canonical name  TopicsInManifoldTheory 
Date of creation  20130322 14:11:04 
Last modified on  20130322 14:11:04 
Owner  evin290 (5830) 
Last modified by  evin290 (5830) 
Numerical id  15 
Author  evin290 (5830) 
Entry type  Topic 
Classification  msc 5300 