topics in manifold theory
A manifold is a space that is
locally like , however lacking a preferred system of
coordinates. Furthermore, a manifold can have global topological
properties, such as non-contractible loops (http://planetmath.org/Curve), that distinguish it from
the topologically trivial .
By imposing different restrictions on the transition functions of a manifold, one obtain different types of manifolds:
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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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space-time 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 | 2013-03-22 14:11:04 |
Last modified on | 2013-03-22 14:11:04 |
Owner | evin290 (5830) |
Last modified by | evin290 (5830) |
Numerical id | 15 |
Author | evin290 (5830) |
Entry type | Topic |
Classification | msc 53-00 |