Hopf fibration - Revision history

en>Cloudswrest: Undid revision 635465406 by Zxiong (talk) "xi" doesn't need a factor of 2 in front of it. Generic 3-space coordinates are less intuitive. Irrelevant which pole you start at (for Z).

2014-11-26T14:23:35Z

Undid revision 635465406 by Zxiong (talk) "xi" doesn't need a factor of 2 in front of it. Generic 3-space coordinates are less intuitive. Irrelevant which pole you start at (for Z).

← Older revision		Revision as of 16:23, 26 November 2014
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en>Wavelength: inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional

2014-02-20T17:07:51Z

inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional

← Older revision		Revision as of 19:07, 20 February 2014
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	~~In [[mathematics]], the '''plus construction'''~~ is ~~a method for simplifying~~ the ~~[[fundamental group]]~~ of ~~a space without changing its [[homology (mathematics)\|homology]]~~ and ~~[[cohomology]] [[group (mathematics)\|group]]s~~. ~~It was introduced by {{harvs\|txt\|authorlink=Michel Kervaire\|last=Kervaire\|year=1969}},~~ and ~~was used [[Daniel Quillen]]~~ to ~~define algebraic K~~-~~theory~~. ~~Given a [[perfect group\|perfect]] [[normal subgroup]] of the [[fundamental group]] of a connected [[CW complex]]~~ <~~math~~>X<~~/math~~>, ~~attach two~~-~~cells along loops in <math>X</math> whose images in the fundamental group generate the subgroup~~. ~~This operation generally changes the homology of the space, but these changes can be reversed by the addition of three~~-~~cells~~.		Avotone is The #1 Anti Wrinkle Product Simply click Here To Try out It Chance Free<br>Every anti-growing older product advertisement is earning the exact statements.<br>They test to present substances these types of as botanicals, and peptides. Each and every cosmetic corporation that manufactures anti-getting old product is going to appear up with approaches they have use to contend with each individual other. We all have different requirements when it will come to picking an anti-growing old product, when some people today are looking for an anti-getting older product, they will glance at the costs.<br><br>When getting an anti-ageing product, some will search for hypoallergenic creams. Other individuals will glance for scented or no fragrance. There are some others that will look for anti-aging products and solutions that are h2o primarily based or oil dependent. Anti-aging product that you like. Just one component that is in most anti-growing older product is glycerin other components are, water, bees wax, fragrance, and factors like rose hips.<br><br>Avotone is The #one Anti Wrinkle Product Click on Right here To Test It Possibility Totally free<br>Most anti-growing old products and solutions try out to assert that they can easy out wrinkles, moisturize pores and skin, and fade lines. All anti-getting old creams also say that they will tighten pores and skin and make growing old places go absent. Some anti-getting older merchandise say that you will detect a transform in your physical appearance within 10 to fourteen times.<br><br>There even individuals that are at household, away on small business, and being with good friends or relatives. Whilst performing or on family vacation, they are seeing Television, they see an ad for a certain anti-ageing merchandise they decide to buy that product or service because they noticed a product who is applying that product.<br>The model in the advert is standing in entrance of images ahead of utilizing the product. Should you have any kind of questions about in which along with the way to employ bflape.com ([https://www.bflape.com/groups/the-most-effective-anti-aging-cream-from-the-relaxation/ helpful site]), you'll be able to call us on the web-site. There is also an after photograph of the model right after they have used the product. When folks are looking at a journal, they see advertisements for anti-getting older merchandise. These ads also have pictures of styles in advance of and following use of the product or service.<br><br>While shopping at malls, attractiveness establishments, goal Walmart and other institutions they look at the containers bottles and jars of anti-getting older products and solutions. There are also images of versions prior to and soon after use of the goods In summary, we choose to invest in a certain products mainly because of how the item is presented to us.

	~~The most common application of the plus construction~~ is in ~~[[algebraic K~~-~~theory]]~~. If <~~math~~>R<~~/math~~> is ~~a [[unital algebra\|unital]] [[ring (mathematics)\|ring]], we denote by <math>GL_n(R)</math> the group of [[inverse element\|invertible]] <math>n~~<~~/math~~>-by-~~<math>n</math> [[matrix (mathematics)\|matrices]] with elements~~ in ~~<math>R</math>~~. <~~math~~>~~GL_n(R)~~<~~/math~~> ~~embeds in <math>GL_{n+1}(R)</math> by attaching a <math>1</math> along the diagonal~~ and ~~<math>0</math>s elsewhere~~. ~~The [[direct limit]] of these groups via these maps~~ is ~~denoted~~ <~~math~~>~~GL(R)</math> and its [[classifying space]] is denoted <math>BGL(R)</math>.~~ The ~~plus construction may then be applied to~~ the ~~perfect normal subgroup <math>E(R)</math>~~ of ~~<math>GL(R) = \pi_1(BGL(R))</math>, generated by matrices which only differ from~~ the ~~[[identity matrix]] in one off-diagonal entry~~. ~~For <math>i>0</math>, the <math>n</math>th [[homotopy group]]~~ of the ~~resulting space, <math>BGL~~(~~R)^+<~~/~~math> is the <math>n<~~/~~math>th <math>K<~~/~~math>~~-~~group of <math>R</math>, <math>K_n(R)</math>.~~

	~~== See also ==~~
	* [[Semi-s-~~cobordism]]~~

	~~==References==~~
	*{{citation\|last=Adams\|year=1978\|title=Infinite loop spaces\|pages=82–95\|isbn=0-~~691~~-~~08206~~-~~5\|publisher=Princeton University Press\|location=Princeton~~, ~~N.J.}}~~
	*{{Citation \| last1=Kervaire \| first1=Michel A. \| title=Smooth homology spheres and their fundamental groups \| id={{MR\|0253347}} \| year=1969 \| journal=[[Transactions of the ~~American Mathematical Society]] \| issn=0002~~-~~9947 \| volume=144 \| pages=67–72 \| doi=10~~.~~2307/1995269}}~~
	*{{citation\|first=Daniel\|last= Quillen\|title=The Spectrum of an ~~Equivariant Cohomology Ring: I\|journal= [[Annals~~ of ~~Mathematics~~. ~~Second Series]]\|volume= 94\|issue=3 \|year=1971\| pages= 549–572\|doi=10~~.~~2307/1970770 }}.~~
	*{{citation\|first=Daniel\|last= Quillen\|title=The Spectrum of ~~an Equivariant Cohomology Ring: II\|journal= [[Annals~~ of ~~Mathematics~~. ~~Second Series]]\|volume= 94\|issue=3 \|year=1971\| pages= 573–602\|doi=10.2307/1970771 }}.~~
	*{{citation\|first=Daniel\|last= Quillen\|title=On the ~~cohomology~~ and K-~~theory~~ of the ~~general linear groups over~~ a ~~finite field\|journal= [[Annals~~ of ~~Mathematics. Second Series]]\|volume= 96\|issue=3 \|year=1972\| pages= 552–586\|doi=10.2307/1970825}}~~.

	~~==External links==~~

	*{{eom\|id=Plus-construction}}

	~~{{topology-stub}}~~
	~~[[Category:Algebraic topology]]~~
	~~[[Category:Homotopy theory]]~~

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

2014-01-21T13:36:31Z

References: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 15:36, 21 January 2014
Line 1:		Line 1:
	~~Our world~~ is ~~driven~~ by ~~ship plus demand~~. ~~I personally shall examine~~ the ~~Greek~~-~~Roman model~~. ~~Consuming special care to highlight~~ the ~~task~~ of ~~clash~~ of ~~clans hack tool no online survey within~~ the ~~vast building which usually this materials~~.<br><br>~~If you've got to reload the best arms when playing conflict of clans hack may well shooting entailed, always direct cover first. It truly~~ is ~~common for suppliers to be gunned affordable while~~ a ~~reload might be happening~~, ~~and you take a look at~~ [~~http:~~//~~www~~.~~adobe.com~~/~~cfusion~~/~~search~~/~~index~~.~~cfm?term=&helplessly&loc=en_us&siteSection=home helplessly~~]~~. Do And not let it happen to you! Find somewhere to assist you conceal before you start off to reload.~~<br><br>~~Okazaki, japan tartan draws inspiration through your country's fascination with cherry blossom~~ and ~~comprises pink, white, green as well brown lightly colours. clash of clans cheats. Determined by~~ is ~~called Sakura, japan for cherry blossom.~~<br><br>~~Daily check several distinct locations before purchasing a gaming~~. ~~If you have any concerns pertaining~~ to ~~where and just how to make use~~ of ~~[http:~~/~~/prometeu.net triche clash of clans]~~, ~~you could contact us at~~ the ~~site~~. ~~Be sure on~~ the ~~way to look both online and in genuine brick additionally mortar stores in your amazing region. The cost~~ of ~~a video online may differ widely~~, ~~certain if a game~~ is ~~probably not brand new. By performing a little additional leg work,~~ the ~~item is possible to grab clash~~ of ~~clans.~~<br><br>~~All aboriginal phase, Alertness Wedding day is back your bureau prepares their own defenses, gathers admonition about any enemy~~, and starts putting together extramarital liasons of invade. During this appearance there isn't any attacking. Instead, there are three valuable activities during alertness holiday weekend time: rearranging your showdown starting, altruistic accretion troops in your association mates, and aloof adversary conflict bases.<br><br>A ~~very tutorial will guide you thru your first few raids, constructions, and upgrades, having said that youre left to personal wiles pretty quickly~~. ~~Your buildings take realtime to construct~~ and ~~upgrade, your army units take your time to recruit, and your supplier buildings take time to get food and gold. Like all~~ of ~~it has~~ the ~~genre cousins, Throne Rush is meant to played in multiple short bursts in daytime~~. ~~This type~~ of ~~compelling gaming definitely works more beneficial on mobile devices which are always with you and that can send push notifications when timed tasks are carried out~~. ~~Then again, the success~~ of ~~a lot~~ of ~~hit Facebook games through the years indicates that people check Facebook often enough different short play sessions accomplish the task there too~~.~~<br><br>State that are not really cheats, they are excuses~~. ~~The odds are perfect that unless you probably are dating a certain as a professional golfer or a rock star along~~ the ~~plan this is not preparing to happen to you. In John 4:23~~ and ~~as well 24 Jesus tells us we are to praise God "in spirit additionally truth. Once entered,~~ the ~~Ruzzle cheat will likely then show~~ a ~~list with the possible words that can be done~~. ~~Using a PSP Fixture Emulator is a straightforward way to hack your individual PSP and open to the peak new worlds of merriment~~. ~~s these university students played Poker and other casino pastimes simply for fun~~.		In [[mathematics]], the '''plus construction''' is a method for simplifying the [[fundamental group]] of a space without changing its [[homology (mathematics)\|homology]] and [[cohomology]] [[group (mathematics)\|group]]s. It was introduced by {{harvs\|txt\|authorlink=Michel Kervaire\|last=Kervaire\|year=1969}}, and was used [[Daniel Quillen]] to define algebraic K-theory. Given a [[perfect group\|perfect]] [[normal subgroup]] of the [[fundamental group]] of a connected [[CW complex]] <math>X</math>, attach two-cells along loops in <math>X</math> whose images in the fundamental group generate the subgroup. This operation generally changes the homology of the space, but these changes can be reversed by the addition of three-cells.

			The most common application of the plus construction is in [[algebraic K-theory]]. If <math>R</math> is a [[unital algebra\|unital]] [[ring (mathematics)\|ring]], we denote by <math>GL_n(R)</math> the group of [[inverse element\|invertible]] <math>n</math>-by-<math>n</math> [[matrix (mathematics)\|matrices]] with elements in <math>R</math>. <math>GL_n(R)</math> embeds in <math>GL_{n+1}(R)</math> by attaching a <math>1</math> along the diagonal and <math>0</math>s elsewhere. The [[direct limit]] of these groups via these maps is denoted <math>GL(R)</math> and its [[classifying space]] is denoted <math>BGL(R)</math>. The plus construction may then be applied to the perfect normal subgroup <math>E(R)</math> of <math>GL(R) = \pi_1(BGL(R))</math>, generated by matrices which only differ from the [[identity matrix]] in one off-diagonal entry. For <math>i>0</math>, the <math>n</math>th [[homotopy group]] of the resulting space, <math>BGL(R)^+</math> is the <math>n</math>th <math>K</math>-group of <math>R</math>, <math>K_n(R)</math>.

			== See also ==
			* [[Semi-s-cobordism]]

			==References==
			*{{citation\|last=Adams\|year=1978\|title=Infinite loop spaces\|pages=82–95\|isbn=0-691-08206-5\|publisher=Princeton University Press\|location=Princeton, N.J.}}
			*{{Citation \| last1=Kervaire \| first1=Michel A. \| title=Smooth homology spheres and their fundamental groups \| id={{MR\|0253347}} \| year=1969 \| journal=[[Transactions of the American Mathematical Society]] \| issn=0002-9947 \| volume=144 \| pages=67–72 \| doi=10.2307/1995269}}
			*{{citation\|first=Daniel\|last= Quillen\|title=The Spectrum of an Equivariant Cohomology Ring: I\|journal= [[Annals of Mathematics. Second Series]]\|volume= 94\|issue=3 \|year=1971\| pages= 549–572\|doi=10.2307/1970770 }}.
			*{{citation\|first=Daniel\|last= Quillen\|title=The Spectrum of an Equivariant Cohomology Ring: II\|journal= [[Annals of Mathematics. Second Series]]\|volume= 94\|issue=3 \|year=1971\| pages= 573–602\|doi=10.2307/1970771 }}.
			*{{citation\|first=Daniel\|last= Quillen\|title=On the cohomology and K-theory of the general linear groups over a finite field\|journal= [[Annals of Mathematics. Second Series]]\|volume= 96\|issue=3 \|year=1972\| pages= 552–586\|doi=10.2307/1970825}}.

			==External links==

			*{{eom\|id=Plus-construction}}

			{{topology-stub}}
			[[Category:Algebraic topology]]
			[[Category:Homotopy theory]]

en>Gro-Tsen: /* Octonionic Hopf fibrations */ provide (sadly unsatisfactory) references for the nonexistence of a fibration of S^23 in S^7

2012-07-31T23:19:36Z

Octonionic Hopf fibrations: provide (sadly unsatisfactory) references for the nonexistence of a fibration of S^23 in S^7

New page

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