Beta Apodis - Revision history

en>Kogge: wikilink Monthly Notices of the Royal Astronomical Society

2014-03-30T16:28:46Z

wikilink Monthly Notices of the Royal Astronomical Society

← Older revision		Revision as of 18:28, 30 March 2014
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	~~{{Expert-subject\|Mathematics\|date=February 2009}}~~		Oscar is what my wife loves to contact me and I totally dig that title. What I love doing is taking part in baseball but I haven't produced a dime with it. North Dakota is our birth place. Since she was eighteen she's been operating as a receptionist but her promotion never arrives.<br><br>My webpage [http://ddaybeauty.com/node/14766 ddaybeauty.com]
	~~In mathematics, a ''~~'~~handle decomposition of~~ a ~~3-manifold''' allows simplification of the original [[3-manifold]] into pieces which are easier to study~~. ~~An important method used to decompose into [[handlebody\|handlebodies]]~~ is ~~the [[Heegaard splitting]], which gives us~~ a ~~decomposition in two handlebodies of equal genus~~.<~~ref~~>~~{{cite book\|title=[[Quantum invariant\|Quantum Invariants]] of Knots and 3-manifolds\|first=Vladimir G. \|last=Turaev\|publisher=Walter de Gruyter\|year= 1994\|isbn=3-11-013704-6}}~~<~~/ref~~>

	As an example: [[lens space]]s are orientable 3-spaces, and allow decomposition into two '''solid-tori''' which are genus-one-handlebodies. The genus one non-orientable space is a space which is the union of two [~~[solid Klein bottle]]s and corresponds to the twisted product of the 2-sphere and the 1-sphere~~: ~~<math>\scriptstyle S^2\tilde{\times}S^1<~~/~~math>~~.

	~~Each orientable 3-manifold is the union of exactly two orientable handlebodies; meanwhile, each non-orientable one needs three orientable handlebodies~~.

	~~The minimal genus of the glueing boundary determines what is known as the [[Heegaard genus]]. For non-orientable spaces an interesting invariant is the [[trigenus\|tri-genus]].~~

	~~==References==~~
	~~{{reflist}}~~

	*J.C. Gómez Larrañaga, W. Heil, V.M. Núñez. ''Stiefel-Whitney surfaces and decompositions of 3-manifolds into handlebodies'', Topology Appl. 60 (1994), 267-280.
	*J.C. Gómez Larrañaga, W. Heil, V.M. Núñez. ''Stiefel-Whitney surfaces and the trigenus of non-orientable 3-manifolds'', Manuscripta Math. 100 (1999), 405-422.

	~~[[Category:3-manifolds]]~~
	~~[[Category:Topology]~~]


	~~{{topology-stub}}~~

en>Monkbot: /* References */Fix CS1 deprecated date parameter errors

2014-01-15T02:43:51Z

References: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 04:43, 15 January 2014
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	~~The title~~ of the ~~author~~ is ~~Figures but it's not~~ the ~~most masucline name out there~~. ~~California is our birth place~~. ~~I am a meter reader~~. ~~What I adore performing~~ is ~~taking part in baseball but I haven't produced~~ a ~~dime with it.~~<br><br>~~my web page~~ ... ~~at home std testing~~ (~~[http://www~~.~~siccus~~.~~net/blog/15356 mouse click~~ the ~~following post~~])		{{Expert-subject\|Mathematics\|date=February 2009}}
			In mathematics, a '''handle decomposition of a 3-manifold''' allows simplification of the original [[3-manifold]] into pieces which are easier to study. An important method used to decompose into [[handlebody\|handlebodies]] is the [[Heegaard splitting]], which gives us a decomposition in two handlebodies of equal genus.<ref>{{cite book\|title=[[Quantum invariant\|Quantum Invariants]] of Knots and 3-manifolds\|first=Vladimir G. \|last=Turaev\|publisher=Walter de Gruyter\|year= 1994\|isbn=3-11-013704-6}}</ref>

			As an example: [[lens space]]s are orientable 3-spaces, and allow decomposition into two '''solid-tori''' which are genus-one-handlebodies. The genus one non-orientable space is a space which is the union of two [[solid Klein bottle]]s and corresponds to the twisted product of the 2-sphere and the 1-sphere: <math>\scriptstyle S^2\tilde{\times}S^1</math>.

			Each orientable 3-manifold is the union of exactly two orientable handlebodies; meanwhile, each non-orientable one needs three orientable handlebodies.

			The minimal genus of the glueing boundary determines what is known as the [[Heegaard genus]]. For non-orientable spaces an interesting invariant is the [[trigenus\|tri-genus]].

			==References==
			{{reflist}}

			*J.C. Gómez Larrañaga, W. Heil, V.M. Núñez. ''Stiefel-Whitney surfaces and decompositions of 3-manifolds into handlebodies'', Topology Appl. 60 (1994), 267-280.
			*J.C. Gómez Larrañaga, W. Heil, V.M. Núñez. ''Stiefel-Whitney surfaces and the trigenus of non-orientable 3-manifolds'', Manuscripta Math. 100 (1999), 405-422.

			[[Category:3-manifolds]]
			[[Category:Topology]]


			{{topology-stub}}

en>Ilvon at 05:57, 28 August 2012

2012-08-28T05:57:18Z

New page

The title of the author is Figures but it's not the most masucline name out there. California is our birth place. I am a meter reader. What I adore performing is taking part in baseball but I haven't produced a dime with it.<br><br>my web page ... at home std testing ([http://www.siccus.net/blog/15356 mouse click the following post])