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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>
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| 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>.
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| Each orientable 3-manifold is the union of exactly two orientable handlebodies; meanwhile, each non-orientable one needs three orientable handlebodies.
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| 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]].
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| ==References==
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| {{reflist}}
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| *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.
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| *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.
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| [[Category:3-manifolds]]
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| [[Category:Topology]]
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| {{topology-stub}}
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Latest revision as of 17:28, 30 March 2014
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.
My webpage ddaybeauty.com