Poincare duality theorem - Revision history

Vipul at 23:45, 21 July 2011

2011-07-21T23:45:30Z

← Older revision		Revision as of 23:45, 21 July 2011
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	<math>H^i(M;R) \to H_{n-i}(M;R)</math>		<math>H^i(M;R) \to H_{n-i}(M;R)</math>

	Poincare duality theorem states that this map is an isomorphism.		The '''Poincare duality theorem states''' that this map is an isomorphism.

	==Related ~~results~~==		==Related facts==

			===Similar facts===

	* [[Alexander duality theorem]]		* [[Alexander duality theorem]]
	* [[Lefschetz duality theorem]]		* [[Lefschetz duality theorem]]

			===Applications===

			* [[Euler characteristic of odd-dimensional compact connected orientable manifold is zero]]

Vipul: 1 revision

2008-05-11T19:57:32Z

1 revision

← Older revision	Revision as of 19:57, 11 May 2008
(No difference)

Vipul at 21:49, 2 December 2007

2007-12-02T21:49:28Z

New page

{{duality theorem}}

==Statement==

Let <math>M</math> be a [[compact connected orientable manifold]]. Choose <math>[M]</math> to be [[fundamental class]] in <math>M</math>. Then the [[cap product]] with <math>[M]</math> defines a map:

<math>H^i(M;R) \to H_{n-i}(M;R)</math>

Poincare duality theorem states that this map is an isomorphism.

==Related results==

* [[Alexander duality theorem]]
* [[Lefschetz duality theorem]]