SNV calling from NGS data: Difference between revisions

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In algebraic topology, a '''complex-orientable cohomology theory''' is a [[multiplicative cohomology theory]] ''E'' such that the restriction map <math>E^2(\mathbb{C}\mathbf{P}^\infty) \to E^2(\mathbb{C}\mathbf{P}^1)</math> is surjective. An element of <math>E^2(\mathbb{C}\mathbf{P}^\infty)</math> that restricts to the canonical generator of the reduced theory <math>\widetilde{E}^2(\mathbb{C}\mathbf{P}^1)</math> is called a '''complex orientation'''. The notion is central to Quillen's work relating cohomology to [[formal group law]]s.{{citation needed|date=October 2013}}<!-- a bit vague -->
 
If <math>\pi_3 E = \pi_5 E = \cdots</math>, then ''E'' is complex-orientable.
 
Examples:
*An ordinary cohomology with any coefficient ring ''R'' is complex orientable, as <math>\operatorname{H}^2(\mathbb{C}\mathbf{P}^\infty; R) \simeq \operatorname{H}^2(\mathbb{C}\mathbf{P}^1;R)</math>.
*A complex ''K''-theory, denoted by ''K'', is complex-orientable, as <math>\pi_3 K = \pi_5 K = \dots = 0.</math> ([[Bott periodicity theorem]])
*[[Complex cobordism]], whose spectrum is denoted by MU, is complex-orientable.
 
A complex orientation, call it ''t'', gives rise to a formal group law as follows: let ''m'' be the multiplication
:<math>\mathbb{C}\mathbf{P}^\infty \times \mathbb{C}\mathbf{P}^\infty \to \mathbb{C}\mathbf{P}^\infty, ([x], [y]) \mapsto [xy]</math>
where <math>[x]</math> denotes a line passing through ''x'' in the underlying vector space <math>\mathbb{C}[t]</math> of <math>\mathbb{C}\mathbf{P}^\infty</math>. Viewing
:<math>E^*(\mathbb{C}\mathbf{P}^\infty) = \varprojlim E^*(\mathbb{C}\mathbf{P}^n) = \varprojlim R[t]/(t^{n+1}) = R[\![t]\!], \quad R =\pi_* E =  \oplus \pi_{2n} E</math>,
let <math>f = m^*(t)</math> be the pullback of ''t'' along ''m''. It lives in
:<math>E^*(\mathbb{C}\mathbf{P}^\infty \times \mathbb{C}\mathbf{P}^\infty) = \varprojlim E^*(\mathbb{C}\mathbf{P}^n \times \mathbb{C}\mathbf{P}^m) = \varprojlim R[x,y]/(x^{n+1},y^{m+1}) = R[\![x, y]\!]</math>
and one can show it is a formal group law (e.g., satisfies associativity).
 
== References ==
*M. Hopkins, [http://people.virginia.edu/~mah7cd/Foundations/coctalos.pdf Complex oriented cohomology theory and the language of stacks]
*J. Lurie, [http://www.math.harvard.edu/~lurie/252x.html Chromatic Homotopy Theory (252x)]
 
[[Category:Algebraic topology]]
[[Category:Cohomology theories]]
 
{{topology-stub}}

Latest revision as of 01:48, 13 December 2014



The Chevrolet Silverado Crew Cab LT2 is 3rd workout in the ranking. It has a high engine capacity along with the consumption is efficient. It's the cheapest of these trucks. Its off-road performance is exceptional and it's lower for stability in fact it i balanced to allow it to help at top speed even while carrying to capacity. Group of favorite enable you to people since has good transmission it's affordable. Is actually also used both as a SUV so a truck since there is enough space for 5 passengers.

Brian Ickler will make his begin of 2011 in the Kyle Busch Motorsports #18 Dollar General Toyota Tundra at Texas Motor Speedway on Friday, June 10. The WinStar World Casino 400K is being run in conjunction with the IZOD IndyCar Series Twin 275s on Saturday, June eleventh.



Chrysler also makes vans where the seats from the back rotate backwards. That option could be ideal for anyone who has children or adults who desire to adjust their seat incline while they travel. Excellent for sleeping, and also for just getting comfortable during a long adventure.

2007 Tundra, which was released at the Chicago Auto Show, is produced larger than Chevrolet Silverado, Ford F-Series, Nissan Titan and Dodge Ram- its mighty rivals in the truck segment. Most up-to-date model boasts that the enhanced protect off road parts paved way for greater towing capacity and truck general performance. There are 3 available engine choices - contemplate.0 L V6, 4.7 L V8, and new 5.7 L V8.

Let me coach you for 3 months, risk-free. Follow my trades because make them live around. I'll let you follow the trades I make inside my elite hedge fund. Many wealthy, savvy and very connected investors invest a minimum of $5 million to get started on my fund, and pay me at least $100,000 in a year's time to make these trades for them - but in Macro Millionaire, you can trade alongside me.

2010 Honda CR-V-Balance. toyota tundra off road That is what the Honda CR-V possesses that its competition doesn't. Interior packaging and build quality are first rate, the 180 horsepower 4-cylinder is surprisingly punchy and efficient and through it all of the CR-V remains affordable. Here is the mix of frugality, practicality and sportiness that Honda does much better anyone similar.

Get all the steps on Macro Millionaire toyota tundra tuning final coaching program or trading service you'll ever need! If you think that's hype, you should read lifestyle altering experience Jim had by just following within just Just one of the nine different parts of Macro Millionaire I construct in the video.

ClarendonCounty is holding a bass tournament this week at Lake Marion. Bass anglers from over spain are beginning to this area to want the record $100,000.00 dollar pay work day! Approximately 200 boaters will be out on their own water from November 9 until the 12th, and also the final weigh all the way through. Local anglers Travis Jackson and Ray Winans in order to be in the area.

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