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| {{Unreferenced|date=December 2009}}
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| In [[mathematics]], a [[closure (mathematics)|closed]] ''n''-[[manifold]] ''N'' [[embedding|embedded]] in an (''n'' + 1)-manifold ''M'' is '''boundary parallel''' (or '''∂-parallel''', or '''peripheral''') if there is an [[Homotopy#Isotopy|isotopy]] of ''N'' onto a [[Boundary (topology)|boundary]] [[connected space|component]] of ''M''.
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| ==An example==
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| Consider the [[Annulus (mathematics)|annulus]] <math>I\times S^1</math>. Let π denote the projection map
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| :<math>\pi:I\times S^1\rightarrow S^1,\qquad(x,z)\mapsto z.</math>
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| If a circle ''S'' is embedded into the annulus so that π [[Restriction#Restrictions and extensions|restricted]] to ''S'' is a [[bijection]], then ''S'' is boundary parallel. (The [[Converse (logic)|converse]] is not true.)
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| If, on the other hand, a circle ''S'' is embedded into the annulus so that π restricted to ''S'' is not [[Surjection|surjective]], then ''S'' is not boundary parallel. (Again, the converse is not true.)
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| [[Image:Annulus.circle.pi 1-injective.png|thumb|left|An example wherein π is not bijective on ''S'', but ''S'' is ∂-parallel anyway.]][[Image:Annulus.circle.bijective-projection.png|thumb|left|An example wherein π is bijective on ''S''.]][[Image:Annulus.circle.nulhomotopic.png|thumb|left|An example wherein π is not surjective on ''S''.]]{{Clear}}
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| {{DEFAULTSORT:Boundary Parallel}}
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| [[Category:Geometric topology]]
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Latest revision as of 23:26, 26 February 2014
Her title is Felicidad Ahmad. Bookkeeping has been his day occupation for a whilst. Arizona has usually been my living place but my wife wants us to transfer. To play croquet is some thing that I've done for many years.
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