Bell series - Revision history

Deltahedron: ce

2014-09-22T16:56:24Z

← Older revision		Revision as of 18:56, 22 September 2014
Line 1:		Line 1:
	~~In [[mathematics]], the '''knot complement''' of~~ a ~~[[tame knot]] ''K'' is~~ the ~~three-dimensional space surrounding the knot. To make this precise~~, ~~suppose that ''K'' is a knot in a three-manifold ''M'' (most often~~, ~~''M''~~ is the [[3-~~sphere]]).~~ ~~Let ''N'' be a thickened neighborhood of ''K''; so ''N''~~ is a ~~[[solid torus]]~~. The ~~knot complement is then~~ the [~~[complement (set theory)\|complement]~~] of ~~''N'',~~		Luke Bryan is usually a superstar while in the producing as well as job development initial 2nd to his 3rd studio recording, And , is definitely the evidence. He [http://www.senatorwonderling.com luke bryan tour with] broken on the scene in 2003 together with his [http://lukebryantickets.iczmpbangladesh.org luke bryan concert tour schedule] amusing mixture of downward-residence ease of access, movie celebrity great appears and lyrics, is scheduled t within a significant way. The latest recor around the land graph and #2 [http://minioasis.com upcoming luke bryan concerts] around the take charts, earning it the second highest very first in those days of 2013 for the nation designer. <br><br><br><br>The boy of the , knows patience and determination are key elements with regards to an effective job- . His initially record, Stay Me, created the Top reaches “All My Friends “Country and Say” Gentleman,” when his energy, Doin’ Point, located the artist-a few right No. 7 single men and women: In addition Getting in touch with Is actually a Excellent Factor.”<br><br>Within the tumble of 2005, Tour: Luke & that had a remarkable listing of , including City. “It’s much like you’re receiving a approval to look to the next level, claims all those musicians that have been an element of the Tourabove in a larger amount of performers.” It twisted among the [http://www.museodecarruajes.org jason aldean tickets] most successful trips in their 10-calendar year history.<br><br>Here is my blog post; jason aldean concert ([http://www.banburycrossonline.com just click the up coming document])
	~~:<math>X_K = M - \mbox{interior}(N)~~.<~~/math>~~

	~~The knot complement ''X<sub~~>K<~~/sub~~>~~'' is a [[compact space\|compact]] [[3-manifold]]; the boundary of ''X~~<~~sub~~>K<~~/sub~~>~~'' and the boundary~~ of the ~~neighborhood ''N''~~ are ~~homeomorphic~~ to ~~a two~~-~~[[torus]]~~. ~~Sometimes~~ the ~~ambient manifold ''M'' is understood to be [[3-sphere]]. Context is needed to determine the usage.~~ ~~There are analogous definitions of '''[[link (knot theory)\|link]] complement'''.~~

	~~Many [[knot invariant]]s~~, ~~such as the [[knot group]]~~, ~~are really invariants of~~ the ~~complement of the knot~~. ~~When~~ the ~~ambient space is the three-sphere no information is lost~~: ~~the [[Gordon~~&~~ndash;Luecke theorem]] states~~ that a ~~knot is determined by its complement~~. ~~That is, if ''K'' and ''K''′ are two knots with [[homeomorphic]] complements then there is~~ a ~~homeomorphism of the three-sphere taking one knot~~ to the ~~other.~~

	~~==See also==~~
	~~[[Seifert surface]]~~

	~~==Further reading==~~
	* C. Gordon and J. Luecke, ~~"Knots are determined by their Complements", ''[[Journal~~ of the ~~American Mathematical Society\|J~~. ~~Amer~~. ~~Math~~. ~~Soc~~.~~]]'', '''2'''~~ (~~1989), 371–415.~~

	~~{{Knot theory\|state=collapsed}}~~

	[[~~Category~~:~~Knot theory~~]]

	~~{{knottheory-stub}}~~

en>K9re11: /* Examples */

2014-01-22T17:26:26Z

Examples

← Older revision		Revision as of 19:26, 22 January 2014
Line 1:		Line 1:
	~~The writer~~'~~s name~~ is ~~Christy Brookins~~. ~~Her family members life~~ in ~~Ohio~~. ~~I am truly fond~~ of ~~to go to karaoke but I~~'~~ve been taking on new issues lately~~. ~~Office supervising~~ is ~~where her main income arrives from but she~~'~~s currently utilized for another one~~.<br><br>~~Here~~ is ~~my blog post :: good psychic~~ ([~~http~~:~~//www~~.~~rusload~~.~~de/uprofile~~.~~php?UID=425591 http://www~~.~~rusload~~.~~de/uprofile~~.~~php?UID~~=~~425591~~])		In [[mathematics]], the '''knot complement''' of a [[tame knot]] ''K'' is the three-dimensional space surrounding the knot. To make this precise, suppose that ''K'' is a knot in a three-manifold ''M'' (most often, ''M'' is the [[3-sphere]]). Let ''N'' be a thickened neighborhood of ''K''; so ''N'' is a [[solid torus]]. The knot complement is then the [[complement (set theory)\|complement]] of ''N'',
			:<math>X_K = M - \mbox{interior}(N).</math>

			The knot complement ''X<sub>K</sub>'' is a [[compact space\|compact]] [[3-manifold]]; the boundary of ''X<sub>K</sub>'' and the boundary of the neighborhood ''N'' are homeomorphic to a two-[[torus]]. Sometimes the ambient manifold ''M'' is understood to be [[3-sphere]]. Context is needed to determine the usage. There are analogous definitions of '''[[link (knot theory)\|link]] complement'''.

			Many [[knot invariant]]s, such as the [[knot group]], are really invariants of the complement of the knot. When the ambient space is the three-sphere no information is lost: the [[Gordon–Luecke theorem]] states that a knot is determined by its complement. That is, if ''K'' and ''K''′ are two knots with [[homeomorphic]] complements then there is a homeomorphism of the three-sphere taking one knot to the other.

			==See also==
			[[Seifert surface]]

			==Further reading==
			* C. Gordon and J. Luecke, "Knots are determined by their Complements", ''[[Journal of the American Mathematical Society\|J. Amer. Math. Soc.]]'', '''2''' (1989), 371–415.

			{{Knot theory\|state=collapsed}}

			[[Category:Knot theory]]

			{{knottheory-stub}}

en>Luckas-bot: r2.7.1) (Robot: Adding ca:Sèrie de Bell

2012-02-04T11:14:28Z

r2.7.1) (Robot: Adding ca:Sèrie de Bell

New page

The writer's name is Christy Brookins. Her family members life in Ohio. I am truly fond of to go to karaoke but I've been taking on new issues lately. Office supervising is where her main income arrives from but she's currently utilized for another one.<br><br>Here is my blog post :: good psychic ([http://www.rusload.de/uprofile.php?UID=425591 http://www.rusload.de/uprofile.php?UID=425591])