en>BattyBot: merged templates into Template:Multiple issues using AWB (8323)

2012-09-03T21:03:39Z

merged templates into Template:Multiple issues using AWB (8323)

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	~~Greetings! I am Marvella~~ and ~~I feel comfy when individuals use~~ the ~~complete title~~. ~~One~~ of the ~~very very best issues in the globe for me~~ is ~~to do aerobics~~ and ~~now I'm attempting~~ to ~~make money with it~~. ~~Years in~~ the ~~past we moved to North Dakota. Hiring has been my profession for some time but I~~'~~ve already utilized for another one.~~<br><br>~~Stop~~ by ~~my web page home std test kit~~ ([http://www.~~animecontent~~.~~com~~/~~blog~~/~~348813 relevant web site~~])		In [[mathematics]], the '''Weeks manifold''', sometimes called the '''Fomenko–Matveev–Weeks manifold''', is a closed [[hyperbolic 3-manifold]] obtained by (5, 2) and (5, 1) [[Dehn surgery\|Dehn surgeries]] on the [[Whitehead link]]. It has volume approximately equal to 0.9427... and {{harvtxt\|Gabai\|Meyerhoff\|Milley\|2009}} showed that it has the smallest volume of any closed orientable hyperbolic 3-manifold. The manifold was independently discovered by {{harvtxt\|Weeks\|1985}} and {{harvtxt\|Matveev\|Fomenko\|1988}}.

			Since the Weeks manifold is an [[arithmetic hyperbolic 3-manifold]], its volume can be computed using its arithmetic data and a formula due to [[Armand Borel\|A. Borel]]:

			: <math>\frac{3 \cdot23^{3/2}\zeta_k(2)}{4\pi^4},</math>

			where ''k'' is the [[number field]] generated by ''θ'' satisfying ''θ''<sup> 3</sup> − ''θ'' + 1 = 0 and ''ζ''<sub> ''k''</sub> is the [[Dedekind zeta function]] of ''k'' {{harvs \| last1=Chinburg \| first1=Ted \| last2=Friedman \| first2=Eduardo \| last3=Jones \| first3=Kerry N. \| last4=Reid \| first4=Alan W. \| title=The arithmetic hyperbolic 3-manifold of smallest volume \| mr=1882023 \|zbl = 1008.11015 \| year=2001 \| journal=Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV \| volume=30 \| issue=1 \| pages=1–40}}

			The cusped hyperbolic 3-manifold obtained by (5, 1) Dehn surgery on the Whitehead link is the so-called sibling manifold, or sister, of the [[figure eight knot (mathematics)\|figure eight knot]] complement. The figure eight knot's complement and its sibling have the smallest volume of any orientable, cusped hyperbolic 3-manifold. Thus the Weeks manifold can be obtained by hyperbolic Dehn surgery on one of the two smallest orientable cusped hyperbolic 3-manifolds.

			==References==
			*{{citation
			\| last1 = Agol \| first1 = Ian
			\| last2 = Storm \| first2 = Peter A.
			\| last3 = Thurston \| first3 = William P. \| author3-link = William Thurston
			\| arxiv = math.DG/0506338
			\| doi = 10.1090/S0894-0347-07-00564-4
			\| mr = 2328715
			\| issue = 4
			\| journal = [[Journal of the American Mathematical Society]]
			\| pages = 1053–1077
			\| title = Lower bounds on volumes of hyperbolic Haken 3-manifolds (with an appendix by Nathan Dunfield)
			\| volume = 20
			\| year = 2007}}.
			*{{Citation \| last1=Chinburg \| first1=Ted \| last2=Friedman \| first2=Eduardo \| last3=Jones \| first3=Kerry N. \| last4=Reid \| first4=Alan W. \| title=The arithmetic hyperbolic 3-manifold of smallest volume \| url=http://www.numdam.org/item?id=ASNSP_2001_4_30_1_1_0 \| mr=1882023 \| year=2001 \| journal=Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV \| volume=30 \| issue=1 \| pages=1–40}}
			*{{Citation \| last1=Gabai \| first1=David \| author1-link=David Gabai \| last2=Meyerhoff \| first2=Robert \| last3=Milley \| first3=Peter \| title=Minimum volume cusped hyperbolic three-manifolds \| arxiv=0705.4325 \| doi=10.1090/S0894-0347-09-00639-0 \| mr=2525782 \| year=2009 \| journal=[[Journal of the American Mathematical Society]] \| volume=22 \| issue=4 \| pages=1157–1215}}
			*{{Citation \| last1=Matveev \| first1=S. V. \| last2=Fomenko \| first2=A. T. \| author2-link=Anatoly Fomenko \| title=Isoenergetic surfaces of Hamiltonian systems, the enumeration of three-dimensional manifolds in order of growth of their complexity, and the calculation of the volumes of closed hyperbolic manifolds \|doi=10.1070/RM1988v043n01ABEH001554 \| mr=937017 \| year=1988 \| journal=Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk \| volume=43 \| issue=1 \| pages=5–22}}
			*{{citation\|first=Jeffrey\|last= Weeks\|authorlink=Jeffrey Weeks (mathematician)\|title=Hyperbolic structures on 3-manifolds\|publisher= Princeton Univ.\|series= Ph.D. thesis\|year= 1985}}

			[[Category:3-manifolds]]
			[[Category:Hyperbolic geometry]]


			{{geometry-stub}}

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2012-06-11T21:28:53Z

Dating maintenance tags: {{Inline}} {{Refimprove}} {{Context}}

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Greetings! I am Marvella and I feel comfy when individuals use the complete title. One of the very very best issues in the globe for me is to do aerobics and now I'm attempting to make money with it. Years in the past we moved to North Dakota. Hiring has been my profession for some time but I've already utilized for another one.<br><br>Stop by my web page home std test kit ([http://www.animecontent.com/blog/348813 relevant web site])

Hybrid algorithm (constraint satisfaction) - Revision history

en>BattyBot: merged templates into Template:Multiple issues using AWB (8323)

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