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Topic: CW complex

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	CW complex - Wikipedia, the free encyclopedia
		In topology, a CW complex is a type of topological space introduced by J.H.C. Whitehead to meet the needs of homotopy theory.
		The idea was to have a class of spaces that was broader than simplicial complexes (we could say now, had better categorical properties); but still retained a combinatorial nature, so that computational considerations were not ignored.
		A general cell complex would be a topological space X that is covered by cells; or to put it another way, we start with a space that is the disjoint union of some collection of cells, and take X as a quotient space, for some equivalence relation.
	en.wikipedia.org /wiki/CW_complex (1022 words)

	Re: Fibrations
		CW complexes and cellular maps, much more promising, although also very very intricate and leading soon to highly complex and heavy algebra.
		A typical cofibration is the inclusion map of a subcomplex of a CW complex in the full complex.
		This is dual to the filtration of a CW complex by its skeleta and leads to spectral sequences.
	www.lns.cornell.edu /spr/1999-11/msg0019178.html (414 words)

	CW complex (Site not responding. Last check: 2007-11-07)
		The idea was to have a of spaces that was broader than simplicial complexes (we could say now had better categorical properties); but still retained a combinatorial so that computational considerations were not ignored.
		The homotopy category of CW complexes is the opinion of some experts the best not the only candidate for the homotopy category.
		Auxiliary constructions may mean that spaces that not CW complexes must be used on but half a century since Whitehead has this definition of homotopy category in good One basic result is that the representable functors on the homotopy category have a characterisation (the Brown representability theorem).
	www.freeglossary.com /CW_complex (963 words)

	[No title]
		The complex E consists of one free A-orbit of * *0-cells, four free orbits of 1-cells, and four free orbits of 2-cells.
		The model for B_C consisting of E=C has one 0-cell, two 1-cells and two 2-c* ells, and is the presentation complex* for the presentation : This is a presentation for the trivial group, and hence the 2-complex E=C is co* *ntractible as claimed.
		The Coxeter presentation for G may be encoded as a simplicial complex, K =* * K(G), whose vertices are the Coxeter generators for G and whose simplices are sets of* * commuting generators.
	hopf.math.purdue.edu /Leary-Nucinkis/ijlbeanCW.txt (5614 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		With rergard to inverse limits in the category of spaces, it is clear that the inverse limit of CW complexes does not have to be the homotopy type of a CW complex.
		The homology is not finitely generated, but if this were homotopy equivalent to a CW complex, the image of such an equivalence would lie in a finite subcomplex, being compact.
		The notion of a CW complex dates from a 1949 article by JHC Whitehead, and examples like this seem to have been known from the beginning.
	www.lehigh.edu /dmd1/public/www-data/nk59.txt (406 words)

	[The Harborsite] Substance 33 (Site not responding. Last check: 2007-11-07)
		Mirzayanov maintained that all American CW agent detection equipment operated on the principle of what he called "ion mobility spectroscopy." He declared such equipment is designed and configured to detect a certain number of known CW agents.
		He is intimately familiar with CW agent detection techniques and with the Soviet chemical weapons complex. I spoke with Mirzayanov in early 1996 about Novichok and the possible use of Soviet CW agents during the Persian Gulf War.
		CW agent detection equipment just cannot detect agents in solid form (so-called andquot;dustyandquot; agents). Substance 33 could also have been mixed with sand particles and transported by the wind to soldiers, while remaining undetected.
	grunt.space.swri.edu /pipermail/harborsite/2003-January/001051.html (4765 words)

	CW in TutorGig Encyclopedia (Site not responding. Last check: 2007-11-07)
		Encyclopedia results for CW is an abbreviation which may stand for Continuous wave, a method of radio transmission.
		A continuous wave CW is an electromagnetic wave of constant amplitude and frequency and in mathematical...
		The objects of the category of spectra are sequences E sub n sup of CW complexes as pointed space..
	www.tutorgig.com /es/CW (936 words)

	Complex Weavers Library History (Site not responding. Last check: 2007-11-07)
		The CW Lending Library began with a proposal by CW President Sigrid Piroch at the 1988 CW Seminar in Lake Forest, IL.
		CW Early Weaving Books on CD This is your opportunity to have a weaving rare book library on your computer.
		CW is making available CD-ROMs [Windows, Max, and Linux compatible] conatining a number of early printed weaving books including Franz Donat's 9015 patterns, John Murphy's Treatise on the Art of Weaving, the 18th century pattern books of J M Frickinger and J M Kirschbaum, and many other difficult to obtain books.
	www.complex-weavers.org /libhist.htm (592 words)

	Eilenberg-MacLane space -- In mathematics, an Eilenberg-MacLane space is a s... (Site not responding. Last check: 2007-11-07)
		Then an Eilenberg—MacLane space exists, as a CW complex, and is unique up to a weak homotopy equivalence.
		A K(π,n) can be constructed stage-by-stage, as a CW complex, starting with a wedge of spheres, one for each generator of the group π, and adding cells in (possibly infinite number of) higher dimensions so as to kill all extra homotopy.
		Every CW complex possesses a Postnikov tower, that is, it is homotopy equivalent to an iterated fibration with fibers the Eilenberg—Mac Lane spaces.
	eilenberg-maclane-space.en.tracking24.net (312 words)

	Complex Weavers Awards Page (Site not responding. Last check: 2007-11-07)
		Complex Weavers is pleased to announce a award to be given for excellence in complex weaving at juried shows.
		Requests for the award or information about the award should be sent to the CW vice president, Carolyn Gritzmaker drawloom50@yahoo.com, preferably by email or with an email contact.
		In return, CW asks for a description of the piece and a slide and/or photograph that will be copied for the new slide kit, for the gallery on the website and the archives.
	www.complex-weavers.org /awards.htm (367 words)

	Re: orbifolds - a simple example in R^2? (Site not responding. Last check: 2007-11-07)
		CW complexes are made out of simpler pieces - balls as opposed to manifolds - but we allow the pieces to be stuck together in more general ways.
		Also, the pieces of a CW complex are always closed, while in a stratified space the top stratum is open - and then when we remove that, the next stratum is open, and so on.
		Stratified spaces are good when you want to do differential topology on something a bit more singular than a manifold, while CW complexes are designed for doing homotopy theory.
	www.lns.cornell.edu /spr/1999-02/msg0014413.html (296 words)

	Cw Complex - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-07)
		The topology of CW complexes (The University series in higher mathematics)
		Finite Group Actions on Simply-Connected Manifolds and Cw Complexes (Memoirs of the American Mathematical Society, 257)
		Combinatorial Homotopy and 4-Dimensional Complexes (De Gruyter Expositions in Mathematics)
	encyclopedia.worldsearch.com /cw_complex.htm (88 words)

	Complex Weavers Sharing Information - Encouraging Interests (Site not responding. Last check: 2007-11-07)
		Complex Weavers is open to anyone with a curiosity to know and a willingness to share.
		In weaving, complex does not have to be defined as difficult.
		Complex Weavers Seminar is a three-day conference held in even numbered years that further encourages exchange of information and formation of many friendships.
	www.complex-weavers.org (839 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Simplicial sets used to be called complete semisimplicial complexes(css complexes); the word complete referred to the incorporation of degeneracy operations with the face operations, so a semisimplicial complex only had face operators (i.e, the hom sets in the domain category consisted of strict monomorphisms [n]--->[m]).
		It was the following: 1) The barycentric subdivision of a semisimplicial CW complex is a regular semisimplicial CW complex.
		2) The barycentric subdivision of a regular semisimplicial CW complex is a (geometrical) simplicial complex.
	www.lehigh.edu /~dmd1/bg13.txt (727 words)

	Compactly generated space - Wikipedia, the free encyclopedia
		There have been various attempts to remedy this situation, one of which is to restrict oneself to the full subcategory of compactly generated Hausdorff spaces, that is, compactly generated spaces which are also Hausdorff.
		The category of compactly generated Hausdorff spaces is general enough to include all metric spaces, topological manifolds, and all CW complexes.
		Given any topological space X we can define a (possibly) finer topology on X which is compactly generated.
	en.wikipedia.org /wiki/Compactly_generated_space (371 words)

	CW complex \| TutorGig.co.uk Encyclopedia (Site not responding. Last check: 2007-11-07)
		Classical Music See all 3074 results in CW complex..
		Electronics See all 180 results in CW complex..
		The Logic of Failure: Recognizing and Avoiding Error in Complex Situat..
	www.tutorgig.co.uk /encyclopedia/getdefn.jsp?keywords=CW_complex (1261 words)

	No. 89-1 (Site not responding. Last check: 2007-11-07)
		Verification: While the Libyan plant is a dedicated CW facility, Gadhafi's protestations that it is a pharmaceutical complex nicely illustrates the problem: essentially any facility that actually is meant for production of civilian chemical products (for example, pesticides, fertilizers, and pharmaceuticals) has the inherent ability to produce toxic chemical agents for weapons.
		In fact, the verification problem associated with a CW ban is made even more intractable by the fact that chemical agents (and biological and toxin weapons for that matter) can now be manufactured using commercially available systems that can be located at essentially any facility.
		All financing associated with the construction, equipping and operation of the Libyan CW complex must cease, for example all disbursements under existing loan agreements should be terminated and no new supplier credits offered.
	www.security-policy.org /papers/1989/89-1.html (1258 words)

	[No title]
		c c Internal variables: complex cgam,czero,d1,d2 real argum,dflval,eps1,eps2,omega1,omega2,phires,rho,sig integer i,i0,i1,i2,j,km,k1,m0,m2 c eps1=eps eps2=eps czero=cmplx(0.,0.) km=k+m k1=k+1 c Make sure that all arguments are in (-pi,pi] call restrc(t,km,pi,twopi) c Define block diagonal matrix W containing eigenvectors of subproblems.
		else argum=4.atan(1.) endif else argum=aimag(clog(z)) endif c return end c---------------------------------------------------------------------------- subroutine defref(w1,w2,wnew,cgam,sig,km) complex* cgam,wnew(),w1(),w2() real sig integer j,km c Performs reflection determined by cgam,sig on old eigenvectors w1(),w2() c to determine new deflated eigenvector wnew() and modified old eigenvector c w1(*) corresponding to undeflated eigenvalue.
		real absz2(),delta,dphi,dt,phi,tdif() complex cfact,czero,w(2,),wnew(2),z() integer j,km c czero=cmplx(0.,0.) wnew(1)=czero wnew(2)=czero do 10 j=1,km if(absz2(j).le.1.)then cfact=z(j)/(1.-cmplx(cos(dt-tdif(j)),sin(dt-tdif(j)))) wnew(1)=wnew(1)+w(1,j)cfact wnew(2)=wnew(2)+w(2,j)cfact endif 10 continue c Normalize wnew call phivl2(phi,dphi,tdif,absz2,km,dt) delta=sqrt(dphi/2.) wnew(1)=wnew(1)/delta wnew(2)=wnew(2)/delta c return end c----------------------------------------------------------------------- subroutine idxord(t,idx,m0) real t() integer i,idx(),itemp,j,m0 logical nochg c Reorders index array idx corresponding to increasing values of t do 20 i=1,m0-1 nochg=.true.
	www.netlib.org /toms/730 (8723 words)

	[No title]
		The rigidity results for these complexes show that the complex of a fixed generic function/hamiltonian is a retract of the Morse (respectively Novikov or Floer) complex of any other sufficiently $C^{0}$ close generic function/hamiltonian.
		In an application to Hamiltonian dynamics we relate the existence of bounded and periodic orbits on non-compact level hypersurfaces of Palais-Smale Hamiltonians with just one singularity which is neat to the lack of self-duality (in the sense of Spanier-Whitehead) of the sublink of the singularity.
		For a simply connected, finite type CW- complex X we introduce a geometric notion of cone-length extending the rational one introduced by Lemaire and Sigrist and we show that it is larger by at most one than the L.S. category.
	www.dms.umontreal.ca /~cornea/abstracts.html (1334 words)

	Schedule (Site not responding. Last check: 2007-11-07)
		The calculation of the homology of CW complexes via the cellular chain complex is a result of both theoretical and practical importance.
		After the first two weeks of the course, you should be able to display the ``exact couple'' associated to the filtraton of the homology of a CW complex, and show how to obtain the cellular chain complex from it.
		You should try to show directly that if the spectral sequence of a double complex collapses one way to the y-axis and the other way to the x-axis, then these two E-2 terms are isomorphic.
	www.math.uiuc.edu /~mando/classes/20012002/431/node2.html (413 words)

	complex equivalences
		Equivalences of real submanifolds in complex space Equivalences of real submanifolds in complex space We show that for any real-analytic submanifold M in C^N there is a proper real-analytic subvariety V contained in M such that for any point p...
		Two determined ambulance men went to the wrong address, grabbed a healthy Norwegian, slapped him onto a stretcher and rushed him to a hospital in Kragero, 40 miles away, despite his vociferous objections.
		Equivalences of Real Submanifolds in Complex Space Equivalences of Real Submanifolds in Complex Space We show that for any real-analytic submanifold M in Ã¢ÂÂN there is a proper real-analytic subvariety V Ã¢ÂÂ M such that for any p Ã¢...
	www.milton-model.com /milton_model/complex-equivalences.html (508 words)

	Abstract (Site not responding. Last check: 2007-11-07)
		We prove that, up to homotopy equivalence, every connected CW-complex is the quotient of a contractible complex by a proper action of a discrete group, and that every CW-complex is the quotient of an aspherical complex by an action of a group of order two.
		The fact that our result concerns homotopy type (whereas the Kan-Thurston theorem concerns homology) is a reflection of the existence of `contractible groups', i.e., groups for which the quotient of the universal proper G-space by G is contractible.
		I don't know whether this result is true or not, but it certainly can't be true that `every finite-dimensional CW-complex is the quotient of a finite-dimensional acyclic complex by an action of a group of order two', since any such space would have to be mod-2 acyclic by Smith theory.
	www.maths.soton.ac.uk /~ijl/abstracts/abs18.html (197 words)

	The UK GulfWeb: OP, Novichock, Soviet Chemical Warfare Agents Novichok and Substance 33 (Site not responding. Last check: 2007-11-07)
		It is also now known that in April 1991, the three top personnel in the Soviet chemical weapons complex were secretly presented the Order of Lenin by Premier Valentin Pavlov for having developed new chemical weapons (1).
		In 1982 the Soviets began a top-secret CW development program code-named Foliant at the State Research Institute of Organic Chemistry and Technology in Moscow (2).
		An advocate of strict controls for all chemical weapons, Fedorov carries on a personal crusade, recently reminding everyone, "In reality, the structure of the Soviet-made V-gas differs from that of American VX-gas (6)." Figure 1, reproduced from his book about the Russian CW complex (7), shows the structures.
	www.gulflink.org /GulfWeb/op/novi.html (2730 words)

	A fine referee report. (Site not responding. Last check: 2007-11-07)
		It can be viewed as a direct application of recursion theoretic concepts to homological algebra.
		It doesn't say anything from a computer science point of view, since it doesn't begin to address the complexity or efficiency of the calculations.
		In other words, don't try to publish a paper about arithmetic today if it does not include, as a corollary, a proof of Riemann's conjecture.
	www-fourier.ujf-grenoble.fr /~sergerar/Papers/asens-report.html (363 words)

	Collapsibility Of ... And Some Related Cw Complexes (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		We show that the regular CW complex \Delta(\Pi n)=Sn is collapsible.
		This allows us to generalize and reprove in a conceptual way several previous results regarding the multiplicity of the trivial character in the Sn...
		27 Complexes of not i-connected graphs - Babson, Bjorner et al.
	citeseer.ist.psu.edu /493427.html (353 words)

	05C: Graph theory
		Among the topics of interest are topological properties such as connectivity and planarity (can the graph be drawn in the plane?); counting problems (how many graphs of a certain type?); coloring problems (recognizing bipartite graphs, the Four-Color Theorem); paths, cycles, and distances in graphs (can one cross the Köningsberg bridges exactly once each?).
		There is a significant number of graph-theoretic topics which are the object of complexity studies in computation (e.g.
		Complexity of graph-isomorphism problem (NP but probably not NP-complete)
	www.math.niu.edu /~rusin/known-math/index/05CXX.html (1204 words)

	Cores of spaces, spectra, and E_infty ring spectra, by P. Hu, I. Kriz, and J.P. May (Site not responding. Last check: 2007-11-07)
		For any space or spectrum Y that is p-local and (n_0-1)-connected and has pi_{n_0}(Y) cyclic, there is a p-local, (n_0-1)-connected ``nuclear'' CW complex or CW spectrum X and a map f : X to Y that induces an isomorphism on pi_{n_0} and a monomorphism on all homotopy groups.
		Nuclear complexes are atomic: a self-map that induces an isomorphism on pi_{n_0} must be an equivalence.
		The construction of X from Y is neither functorial nor even unique up to equivalence, but it is there.
	www.math.uiuc.edu /K-theory/0571 (184 words)

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