Hopf fibration: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older editNewer edit →
en>Monkbot
en>Wavelength
inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional
Line 1: Line 1:
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]]

Revision as of 19:07, 20 February 2014

Avotone is The #1 Anti Wrinkle Product Simply click Here To Try out It Chance Free
Every anti-growing older product advertisement is earning the exact statements.
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.

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.

Avotone is The #one Anti Wrinkle Product Click on Right here To Test It Possibility Totally free
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.

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.
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 (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.

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.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Hopf_fibration&oldid=232324"