en>Werddemer: /* See also */

2013-11-13T20:39:54Z

See also

← Older revision		Revision as of 22:39, 13 November 2013
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	~~Hi there~~. ~~Let me start by introducing~~ the ~~author, her title is Sophia~~. ~~Office supervising~~ is ~~my profession~~. ~~What I adore doing~~ is ~~soccer but I don't have~~ the ~~time recently~~. ~~For~~ a ~~whilst I~~'~~ve been in Mississippi but now I~~'~~m contemplating other choices~~.<br><br>~~Here is my web blog - certified psychics~~ - [~~http:~~//~~srncomm~~.~~com~~/~~blog~~/~~2014~~/08/25/~~relieve~~-~~that~~-~~stress~~-~~find~~-a-~~new~~-~~hobby/ srncomm.com~~] -		In [[geometry]], the '''link''' of a [[vertex (geometry)\|vertex]] of a 2-[[dimension]]al [[simplicial complex]] is a [[Graph theory\|graph]] that encodes information about the local structure of the complex at the vertex.

			It is a [[Graph theory\|graph-theoretic]] analog to a sphere centered at a point.

			== Example ==
			[[File:Tetrahedron.svg\|thumb\|The [[tetrahedron]] is a 2-complex.]]
			[[File:Graphe complet K3.png\|thumb\|The link of a vertex of a tetrahedron is the triangle.]]
			The link of a vertex of a tetrahedron is a triangle – the three vertices of the link corresponds to the three edges incident to the vertex, and the three edges of the link correspond to the faces incident to the vertex. In this example, the link can be visualized by cutting off the vertex with a plane; formally, intersecting the tetrahedron with a plane near the vertex – the resulting cross-section is the link.

			==Definition==
			Let <math>\scriptstyle X</math> be a simplicial complex. The '''link''' <math>\scriptstyle\operatorname{Lk}(v,X)</math> of a vertex <math>\scriptstyle v</math> of <math>\scriptstyle X</math> is the graph constructed as follows. The vertices of <math>\scriptstyle\operatorname{Lk}(v,X)</math> correspond to edges of <math>\scriptstyle X</math> which are incident to <math>\scriptstyle v</math>. Two such edges are [[Adjacent (graph theory)\|adjacent]] in <math>\scriptstyle\operatorname{Lk}(v,X)</math> if they are [[Incidence (geometry)\|incident]] to a common 2-cells at <math>\scriptstyle v</math>. In general, for an [[abstract simplicial complex]] and a face <math>\scriptstyle F</math> of <math>\scriptstyle X </math>, denoted <math>\scriptstyle\operatorname{Lk}(F,X)</math> is the set of faces <math>\scriptstyle G</math> such that G <math> \cap </math> F = <math>\emptyset</math> and G <math> \cup </math> F <math> \in </math> X. Because <math> X </math> is simplicial, there is a set isomorphism between <math>\scriptstyle\operatorname{Lk}(F,X)</math> and <math> X_F = \{G \in X</math> such that F <math>\subset G\}</math>.

			The graph <math>\scriptstyle\operatorname{Lk}(v,X)</math> is often given the [[topology]] of a [[ball (mathematics)\|ball]] of small radius centred at <math>\scriptstyle v</math>.

			==References==
			*{{Citation \| last = Bridson \| first = Martin \| author-link = \| last2 = Haefliger \| first2 = André \| author2-link = André Haefliger \| title = Metric spaces of non-positive curvature \| place = \| publisher = Springer \| year = 1999 \| volume = \| edition = \| url = \| doi = \| id = \| isbn = 3-540-64324-9}}






			{{topology-stub}}
			[[Category:Geometry]]

141.228.106.147: /* Discussion */

2012-08-24T15:51:54Z

Discussion

New page

Hi there. Let me start by introducing the author, her title is Sophia. Office supervising is my profession. What I adore doing is soccer but I don't have the time recently. For a whilst I've been in Mississippi but now I'm contemplating other choices.<br><br>Here is my web blog - certified psychics - [http://srncomm.com/blog/2014/08/25/relieve-that-stress-find-a-new-hobby/ srncomm.com] -

Biconjugate gradient method - Revision history

en>Werddemer: /* See also */

141.228.106.147: /* Discussion */