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Topic: Sheaf space

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coherent sheaf

sheaf theory

sheaf cohomology

invertible sheaf

James Sheafe

locally free sheaf

space associated with a sheaf

sheaf spanned by global sections

Exponential sheaf sequence

Hubble Space Telescope

Euclidean space

Hilbert space

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	PlanetMath: locally ringed space
		The utility of this definition lies in the fact that one can then form constructions in familiar instances of locally ringed spaces which readily generalize in ways that would not necessarily be obvious without this framework.
		Another useful application of locally ringed spaces is in the construction of schemes.
		This is version 10 of locally ringed space, born on 2002-05-01, modified 2005-03-05.
	planetmath.org /encyclopedia/LocallyRingedSpace.html (353 words)

	Orðasafn: S
		sheaf of circles bundin af hringjum, hringabundin, = bundle of circles.
		sheaf of planes knippi af sléttum, sléttuknippi, = bundle of planes, -> pencil of planes.
		sheaf of spheres bundin af hvelum, hvelabundin, = bundle of spheres 1.
	www.hi.is /~mmh/ord/safn/safnS.html (3085 words)

	Sheaf (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, a sheaf is the basic tool for expressing relationships between small regions of a space and large regions.
		Since they form a vector space, it is a sheaf of algebras.
		For example, a space together with a sheaf of rings is called a ringed space.
	en.wikipedia.org /wiki/Sheaf_(mathematics) (5324 words)

	Defense Issues: Volume 12, Number 20-- The Promise of Space Potential for the Future (Site not responding. Last check: 2007-10-13)
		And that the understanding of what space means to us as a nation and the support of all Americans are both critical for making the hard decisions required to realize the full potential of space in the years ahead.
		Commercial space, as I said earlier, will become an economic center of gravity, in my opinion, in the future and as such will be a great source of strength for the United States and other nations in the world.
		The space community's growing "pride of place"' is clearly the result of the recognition of the importance space capabilities delivered daily to the joint warfighter in the United States and space's limitless potential to deliver even more impressive capabilities tomorrow.
	www.defenselink.mil /speeches/1997/di1220.html (2678 words)

	Sheaf (mathematics) - Wikipedia, the free encyclopedia
		Beginning with a topological space X, a sheaf assigns to every region (technically, open set) U of X some data F(U), such as a set, a group, or a ring.
		However, it is possible to move a sheaf from one space to another using a continuous function.
		Two morphisms between sheaves determine a continuous map of the corresponding étalé spaces which is compatible with the projection maps (in the sense that every germ is mapped to a germ over the same point).
	www.reference.com /browse/wiki/Sheaf_space (5324 words)

	Springer Online Reference Works
		Abstract potential theory arose in the middle of the 20th century from the efforts to create a unified axiomatic method for treating a vast diversity of properties of the different potentials that are applied to solve problems of the theory of partial differential equations.
		A harmonic space is locally connected, does not contain isolated points and has a basis consisting of connected resolutive sets (resolutive domains).
		as hyperharmonic sheaf is a harmonic subspace of
	eom.springer.de /p/p074150.htm (1418 words)

	Sheffield City Council
		Sheaf Valley has the potential for dramatic change, therefore, the degree of intervention recommended is Reinvention and Reconfiguration.
		Gateway buildings at Sheaf Square, sited on either side of Howard Street and Surrey Lane, could be used to define the entry to this space.
		Use of manufactured materials in these spaces must not detract from the natural materials palette of the Heart of the City.
	sccplugins.sheffield.gov.uk /urban_design/quarters_sheaf_principles.htm (564 words)

	Springer Online Reference Works
		(this is essential, for example, in algebraic geometry, where the spaces arising are, as a rule, non-separated) and to the fact that other cohomologies (under certain specific conditions) reduce to a sheaf cohomology, at least in those situations where their application is justified.
		The universality property enables one to compare cohomologies arising in concrete situations with sheaf cohomology (and consequently also with each other), to discern for them the natural bounds within which their application is effective, and also to apply sheaf-theoretic methods to the solution of concrete problems.
		Grothendieck and his school vastly generalized sheaf theory, from sheaves on a space to the more general notion of sheaves on a site and that of a topos (cf.
	eom.springer.de /s/s084840.htm (2238 words)

	FM 6-40 Appendix H
		The sheaf front for a circular sheaf is the distance across the center of the circle from burst to burst plus one burst width.
		The sheaf depth is the distance between the center of the foremost and rearmost burst.
		The sheaf depth for a circular sheaf is the distance across the center of the circle from burst to burst plus one burst width.
	www.globalsecurity.org /military/library/policy/army/fm/6-40/Apph.htm (4323 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		I'm always at the sheaf, i stuffed up once by having a fight there with my friends, Bouncers come a stop the fight, they had aworld to me and that was the end of the sitution,If i was in another place i would have got my ass kicked by the bouncers.
		I was very disappointed that a lovely pub like the Sheaf has such violent, power hungry bouncers as I saw last night, I must admit it is not the first time I have witnessed this agro and abondon for their actual purpose at the pub and last night I was quite distressed about thier behaviour.
		The Sheaf should really have a look at thier security and perhaps re-educate them on the purpose of their presence, ie to divert violence not to encourage and precipitate it.
	www.sydneypubguide.net /pubs/Golden_Sheaf.aspx (977 words)

	[No title]
		Remark We have already seen that the spectrum of a commutative ring is a ringed space; that's the motivation for this definition.
		of locally ringed spaces is a morphism with a two-sided inverse.
		The properties of localization show that this is a bijection; by looking at properties of containment, one also sees that it is a homeomorphism.
	odin.mdacc.tmc.edu /~krc/agathos/schem2.html (1105 words)

	week125
		All these moduli spaces are important and interesting, but the moduli space of elliptic curves is a nice simple example when you're first trying to learn this stuff.
		Now, the quotient space H/SL(2,Z) is not a smooth manifold, because while the upper halfplane H is a manifold and the group SL(2,Z) is discrete, the action of SL(2,Z) on H is not free: i.e., certain points in H don't move when you hit them with certain elements of SL(2,Z).
		For any open set U in the moduli space, an object of S(U) is a family of elliptic curves over U, such that each elliptic curve in the family sits over the point in moduli space corresponding to its isomorphism class.
	math.ucr.edu /home/baez/week125.html (2712 words)

	Good Math, Bad Math : Stepping Back a Moment
		In a topological space, we don't care whether we can measure how far it is from a point A to a point B; but we do care whether we can meaningfully ask "Is B closer to A than C?" or "Is A adjacent to B?".
		But the important distinction is that what we were gluing was sections of euclidean spaces - and euclidean spaces have a standard metric, and we describe the glue maps in terms of that standard metric.
		A sheaf of foos (where foo can be all sorts of different kinds of things, like sets, groups, rings...) is a much more general concept.
	scienceblogs.com /goodmath/2006/12/stepping_back_a_moment.php (2506 words)

	Amazon.com: Etale Cohomology. (PMS-33): Books: James S. Milne (Site not responding. Last check: 2007-10-13)
		When reading this section, it is best to think of the fundamental group from ordinary topology in terms of the universal covering space instead of simple connectedness as it is the former concept that is employed to define the fundamental group of a scheme.
		The author turns to sheaf theory in the next chapter and shows how etale topology does give exactness for sequences of sheaves that are not exact in the Zariski topology.
		He convinces the reader right away that the sheaf category is more general than the abelian category by showing that the former does not have enough projectives.
	www.amazon.com /Etale-Cohomology-PMS-33-James-Milne/dp/0691082383 (1820 words)

	Golden Sheaf Hotel Double Bay Hotel & Accommodation Sydney NSW (Site not responding. Last check: 2007-10-13)
		With four distinctly different bars, featuring live entertainment, sporting screens, a beergarden bistro and a sophisticated upstairs bar as a function space, it has it all.
		The top floor of The Golden Sheaf has been refurbished to include nine accommodation rooms, all with ensuites.
		Some of the original heritage items such as the corridors have been retained and the room interiors, although modern, are sympathetic to the era.
	www.goldensheafhotel.com (137 words)

	What IS a superfield, really? \| The String Coffee Table
		It’s a sheaf which arises as a quotient of a scheme by an equivalence relation which is also a scheme.
		The sheaf condition is what allows you to treat these functors as if they were geometric objects; it means you can do your geometry locally.
		In the algebraic setting it is much more important to consider stuff like “etale algebraic spaces” since the Zariski topology which is the only topology in the ordinary sense we can use is a very bad one, for instance, it produces quite useless cohomology groups.
	golem.ph.utexas.edu /string/archives/000763.html (6648 words)

	[No title]
		The notion of a sheaf originated in algebraic topology, although it has been suggested that it goes as far back as studies in the 19th century on the analytic continuation of functions.
		That is, given a topological space X, a sheaf A is a family of abelian groups A_x parameterized by the points of X "continuously".
		Thus it became possible to define a cohomology of a topological space with sheaf coefficients.
	br.endernet.org /~loner/sheaves/topos1.txt (3539 words)

	The Barley Sheaf Players
		Parents/caregivers are expected to attend workshops for children ages 5 and under.
		Due to limited space, we request that parents do not bring non-participating siblings to the theatre.
		Please do not send forms to the Barley Sheaf Post Office box, as they may not be processed in time to meet the registration deadline.
	www.barleysheaf.org /SDESignup.php (234 words)

	funny definition of dimension of a topological space
		The dimension of a space X is one less than the infimum of the orders of refinements of open covers.
		i would guess it applies in general only to noetherian topological spaces, ones in which there is only a finite descendiong chain of closed sets beginnig from any given closed set.
		This relates the topology H^1(C) and the analysis H^0(K) (both due to riemann), to the sheaf cohomology group H^1(O), which illustrates the relation between hartshorne's definition and riemann's definition.
	www.physicsforums.com /showthread.php?t=81747 (1485 words)

	Good Math, Bad Math : Big to Small, Small to Big: Topological Properties through Sheaves (part 1)
		A sheaf is a very general kind of structure that provides ways of mapping or relating local information about a topological space to global information about that space.
		To explore the category theory a little further: once you've seen that a sheaf on a topological space is just a functor (presheaf) which respects certain limits (gluing properties I'm assuming will be described in a later post) there's no reason the course category has to be the poset of subspaces of a topological space.
		Okay, a subspace of a topological space can be identified with the continuous map from the subspace into the whole space.
	scienceblogs.com /goodmath/2006/12/big_to_small_small_to_big_topo.php (2692 words)

	Superpoints \| The String Coffee Table
		The claim now is that, yes, when correctly set up, 0-functors which send super-points to some some superspace obtained from vector bundles over target space yield, in a similar fashion, ordinary de Rham cohomology.
		Such a morphism is simply a continuous map between the two topological spaces together with a morphism of sheaves from the sheaf of rings on the target space to the pushforward of the sheaf of rings on the source space.
		In particular, the supermanifolds of the form R^pq are nothing but ringed spaces (M,O) where M=R^p is simply p-dimensional Euclidean space and where O is the sheaf of smooth functions of R^q times elements of exterior powers of R^q.
	golem.ph.utexas.edu /string/archives/000758.html (1371 words)

	SPACE.com -- Constellation of Crime
		Initially, in fact, many of the star atlases of that era did not depict this star cluster as a celestial hairpiece.
		Indeed, in various star maps of the late Middle Ages the cluster was identified as a rose-wreath or ivy-wreath, and occasionally as a Sheaf of Wheat held in the hands of the nearby constellation Virgo.
		Others saw it as the hair of Sampson, not Berenice, while still others regarded it as a tuft at the end of the tail of Leo, the Lion.
	www.space.com /spacewatch/050527_coma_berenices.html (813 words)

	www.myspace.com/barleysheaf
		Barley Sheaf's Latest Blog Entry [Subscribe to this Blog]
		Thanks to the Barley (Swifty) for again organising a great jam night.
		Millbrook Mud – Barley Sheaf Jam Oct 2006
	www.myspace.com /barleysheaf (306 words)

	Barley Sheaf Farm - Holicong Bed and Breakfast, Pennsylvania, PA Lodging and Accommodations
		Barley Sheaf Farm - Holicong Bed and Breakfast, Pennsylvania, PA Lodging and Accommodations
		You have a beautiful view over the gardens with pool and pond, two queen size beds, cozy sitting corner and inviting bathroom with spacious corner jacuzzi for two and separate shower.
		Relaxing by the Vermont stove or in the two person Jacuzzi makes for a perfect romantic getaway.
	www.partyspace.com /facilitypages/barleysheaf/accommodations.htm (650 words)

	Citations: Critical Dimension of the String Theories and the Dualizing Sheaf on the Moduli Space of (super) Curves - ... (Site not responding. Last check: 2007-10-13)
		Citations: Critical Dimension of the String Theories and the Dualizing Sheaf on the Moduli Space of (super) Curves - Manin (ResearchIndex)
		Yu.I.Manin, "Critical Dimension of the String Theories and the Dualizing Sheaf on the Moduli Space of (super) Curves," Functional Anal.
		Recently, a close cousin of the (chiral) bc system based on vector bundles of higher rank was introduced and some of its properties were studied [6, 7] Since families of the usual system play such a decisive role in string theory, one should thus consider families of these generalized....
	citeseer.ist.psu.edu /context/1919646/0 (209 words)

	The Sheaf - University of Saskatchewan Student Newspaper - Home (Site not responding. Last check: 2007-10-13)
		The Sheaf - University of Saskatchewan Student Newspaper - Home
		For a game that has been around for over thousands of years, poker has gained unprecedented popularity since the turn of the century.
		The first stop would take the team to The Willows, where, as is customary when playing in Regina, the Huskies enjoyed their pre-game breakfast.
	www.thesheaf.com /news/technology/all_students_get_web_space (303 words)

	Our Dogs Publishing Ltd
		Top quality, 5 Generation pedigrees printed on heavyweight paper. Double sided to fold into a sheaf with space for veterinary details etc. Supplied in packs of ten
		10 x 5 Generation pedigrees printed in fl on top quality white paper. Double sided to fold into a sheaf with space for veterinary details etc
		Where possible orders will be sent by return post. If your choice is not in stock we will order it for you - please allow 2 - 3 weeks for this. Thank you
	www.ourdogs.co.uk /acatalog/Main_Menu_DELUXE_PEDIGREE_FORMS_351.html (140 words)

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