Morse theory - Revision history

Karl Jones: /* External links */

2016-04-26T01:07:45Z

‎External links

Karl Jones at 13:28, 6 February 2016

2016-02-06T13:28:07Z

Karl Jones at 10:43, 7 December 2015

2015-12-07T10:43:45Z

Karl Jones: /* See also */

2015-09-15T12:59:16Z

‎See also

Karl Jones: Created page with "In the mathematical field of differential topology, '''Morse theory''' enables one to analyze the topology of a manifold by study..."

2015-09-15T12:59:05Z

Created page with "In the mathematical field of differential topology, '''Morse theory''' enables one to analyze the topology of a manifold by study..."

New page

In the [[Mathematics|mathematical field]] of [[differential topology]], '''Morse theory''' enables one to analyze the [[topological space|topology]] of a [[manifold]] by studying [[differentiable function]]s on that manifold.

(TO DO: expand, organize, cross-reference, illustrate.)

== Description ==

According to the basic insights of [[Marston Morse]], a typical differentiable function on a manifold will reflect the topology quite directly. Morse theory allows one to find [[CW complex|CW structures]] and [[handle decomposition]]s on manifolds and to obtain substantial information about their [[homology (mathematics)|homology]].

Before Morse, [[Arthur Cayley]] and [[James Clerk Maxwell]] had developed some of the ideas of Morse theory in the context of [[topography]]. Morse originally applied his theory to [[geodesic]]s ([[critical point (mathematics)|critical points]] of the energy [[functional (mathematics)|functional]] on paths). These techniques were used in [[Raoul Bott]]'s proof of his [[Bott periodicity theorem|periodicity theorem]].

The analogue of Morse theory for complex manifolds is [[Picard–Lefschetz theory]].

== See also ==

* [[Digital Morse theory]]
* [[Discrete Morse theory]]
* [[Jacobi set]]
* [[Lagrangian Grassmannian]]
* [[Lusternik–Schnirelmann category]]
* [[Mathematics]]
* [[Morse–Smale system]]
* [[Sard's lemma]]
* [[Stratified Morse theory]]

== External links ==

* [https://en.wikipedia.org/wiki/Morse_theory Morse theory] @ Wikipedia

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	* [https://en.wikipedia.org/wiki/Morse_theory Morse theory] @ Wikipedia		* [https://en.wikipedia.org/wiki/Morse_theory Morse theory] @ Wikipedia
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← Older revision		Revision as of 13:28, 6 February 2016
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	In the [[Mathematics\|mathematical field]] of [[differential topology]], '''Morse theory''' enables one to analyze the [[topological space\|topology]] of a [[manifold]] by studying [[differentiable function]]s on that manifold.		In the [[Mathematics\|mathematical field]] of [[differential topology]], '''Morse theory''' enables one to analyze the [[topological space\|topology]] of a [[manifold]] by studying [[differentiable function]]s on that manifold.
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−	~~(TO DO: expand, organize, cross-reference, illustrate.)~~

	== Description ==		== Description ==

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 * [[Digital Morse theory]]
 * [[Discrete Morse theory]]
 * [[Jacobi set]]
 * [[Lagrangian Grassmannian]]
 * [[Lusternik–Schnirelmann category]]
 * [[Mathematics]]
 * [[Morse–Smale system]]
 * [[Sard's lemma]]
 * [[Stratified Morse theory]]
 == External links ==
 * [https://en.wikipedia.org/wiki/Morse_theory Morse theory] @ Wikipedia