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Topic: Exotic sphere

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	[No title]
		It's famous because the map from the total space to the base was the first example of a topologically nontrivial map from a sphere to a sphere of lower dimension.
		In fact, 3 of the exotic spheres in 10 dimensions cannot be given a metric such that the connected component of the isometry group is bigger than U(1) x U(1), so these are quite "bumpy".
		I'm not sure exotic spheres are really relevant to physics, but it would be cool, so I'm glad some people are trying to establish connections.
	www.math.niu.edu /~rusin/known-math/99/exotic (2649 words)

	Choosing you Right Crystal Quartz Stone Sphere
		Quartz sphere are composed of minerals and the colour of the sphere is determined by the element that the mineral was fused upon during their formation under the earth.
		While there are many exotic mineralized crystal available for sale in the market, few comes in spherical form as they are either too small to be polished, break easily during polish or too expensive for design such as gems.
		Spheres sold in shop here are normally AA, A, B and C. Grading is determine by clarify, colour and minimal crack or inclusion; not to confused with hair like crystalline in spheres of phantoms.
	www.angelfire.com /weird2/spheredome/index.html (3625 words)

	Exotic sphere - Wikipedia, the free encyclopedia
		In mathematics, an exotic sphere is a differentiable manifold M, which is homeomorphic to the ordinary sphere, but not diffeomorphic.
		That means that from a topological point of view M is a sphere, but not from the point of view of its differential structure.
		The first exotic spheres were constructed by John Milnor in the case n = 7.
	en.wikipedia.org /wiki/Milnor_sphere (142 words)

	The Planet X collection - wands (Site not responding. Last check: 2007-11-01)
		The sphere is of Rose Quartz inlaid with fifteen cushion pearls and mounted to the handle by a ring of gold spheres.
		The sphere is golden jasper inset with 12 freshwater button pearls, a ring of gold spheres joins the sphere to the handle and another hematite ring is at the bottom of the handle.
		When the sphere is depressed the selenite wand illuminates in electric blue and violet and the stones in the handle glow in all their colours.
	www.manalien.freeserve.co.uk /wands.htm (6206 words)

	Exotic sphere Definition / Exotic sphere Research (Site not responding. Last check: 2007-11-01)
		In mathematics, an exotic sphere is a differential manifold M, such that from a topological point of view M is a sphere A sphere is, roughly speaking, a ball-shaped object.
		But in mathematics, sphere refers to the boundary of a ball, which is "hollow".
		exotic sphere is the only exotic sphere of any dimension which is a biquotient.
	www.elresearch.com /Exotic_sphere (173 words)

	Engineers Discover In Nature Exotic Structures Envisioned By Mathematicians
		Their story begins with the iridescence of opals, which are composed of equal-sized spheres about a micrometer in diameter, or roughly a hundred times smaller than the size of a human hair.
		The spheres are packed into a structure known as the face-centered cubic (FCC) lattice, which is exactly the same arrangement used by grocers to stack oranges or apples.
		Because the opal's constituent spheres are about the size of the wavelength of light, their orderly arrangement diffracts light and causes iridescence.
	www.sciencedaily.com /releases/2003/07/030725081432.htm (1077 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		It was this creation and nullification of exotic matter around the Triad that made the strange void in the middle of the gaseous nebula.
		Exotic matter was one of the Holy Grail’s of modern science.
		But the alien sphere had made it across without damage, a feat thought to be impossible by the scientists.
	www.amaysingstories.com /docs/Copilot.doc (3230 words)

	The Plasma Ball Page (Site not responding. Last check: 2007-11-01)
		The insulator between these two electrodes is the gas inside the glass sphere, the glass sphere itself, and the air outside the glass sphere between the sphere and the second electrode inside the power supply.
		All that's left to do to make the plasma sphere look more like the ones in stores is to shorten the lengths of the wires between the components and draw the sphere a little larger.
		The pulsating field around the glass sphere is strong enough to excite the mercury gas inside the fluorescent bulb, which in turn excites the fluorescent coating on the inside of the glass spiral and makes it glow.
	www.waynesthisandthat.com /plasmaballs2.htm (1216 words)

	S - Polygloss
		An exotic simplex on elliptic bases and uniform edges is a segmentatope, but exotic simplexes can have unequal edges.
		For example, a smooþ dodecahedron is a sphere marked up as a dodecahedron, regardless of þe ambient geometry.
		I use þe terms based on glongotope and #-glome to form spheres between þe circle and þe solid sphere.
	www.geocities.com /os2fan2/gloss/pglosss.html (2363 words)

	Mindpixel Blog: May 2005 (Site not responding. Last check: 2007-11-01)
		I now think the object I have been seeing all these years is a Milnor sphere with a complex fractal attractor [or rather, a very large set of attractors] on its surface--a map.
		Consider the thalmacortical loop is a Milnor sphere generator and that the limbic system stores a seven-dimensional index to points on the thalamocortical hypersurface, where the hippocampus indexes space and time, and the amygdala indexes emotion in Wundt's three dimensional emotional space [Pleasure, Arousal, and Dominance].
		As exotic manifolds are not diffeomorphic, one can argue that quantum amplitudes for gravity formulated as functional integrals should include a sum over not only physically distinct geometries and topologies but also inequivalent differentiable structures.
	www.mindpixel.com /chris/2005_05_01_archive.html (2683 words)

	Sphere Research's Slide Rule Universe - New Slide Rule Cases
		After three prototypes, and numerous test fits and color samples, we think the Sphere Duplex Case is ready for prime time.
		The 100% padded case has a tough nylon cover, inside and out, fully bound edges, an ID window, and velcro flap closure.
		These cases are made in the USA for Sphere by Seamcraft.
	www.sphere.bc.ca /test/cases.html (1170 words)

	[No title]
		It's famous because the map from the total space to the base was the first example of a topologically nontrivial map from a sphere to a sphere of lower dimension.
		In fact, 3 of the exotic spheres in 10 dimensions cannot be given a metric such that the connected component of the isometry group is bigger than U(1) x U(1), so these are quite "bumpy".
		I'm not sure exotic spheres are really relevant to physics, but it would be cool, so I'm glad some people are trying to establish connections.
	math.ucr.edu /home/baez/twf_ascii/week141 (3787 words)

	Imagine the Universe News - 25 November 2002 (Site not responding. Last check: 2007-11-01)
		The neutron star EXO 0748-676 (blue sphere in the image) is part of a binary star system, with its companion star (yellow-red sphere in the image) supplying the fuel for the thermonuclear bursts.
		The neutron star is part of a binary star system named EXO 0748-676, located in the constellation Volans, or Flying Fish, about 30,000 light year away in the Milky Way galaxy, visible in southern skies with a large backyard telescope.
		Cottam and her team determined that EXO 0748-676's mass-to-radius ratio is 0.152 solar masses per kilometer, based on a gravitational redshift measurement of 0.35. This provides the first observational evidence that neutron stars are indeed made of tightly packed neutrons, as predicted by theory estimating mass-radius, density-pressure ratios.
	imagine.gsfc.nasa.gov /docs/features/news/25nov02.html (731 words)

	Middle Woodland Period - Southeastern Prehistory.
		Because of the similarity of earthworks and burial goods found at widely scattered sites in the Southeast and the area north of the Ohio River, it was assumed that a cultural continuity—sometimes referred to as the Hopewellian Interaction Sphere—existed throughout much of the eastern United States.
		As distinct territorial units entered into the trading sphere, their goods would be added to a pool of reciprocal trading items, and they would have access to goods unavailable in their own territory.
		Among the exotic trade items recovered by excavations in both areas were copper panpipes, earspools, bracelets and beads, stone platform pipes, mica figurines, ceramic figures, galena, marine shells, freshwater pearls, and green stone celts.
	www.cr.nps.gov /seac/outline/04-woodland/index-2.htm (2197 words)

	David Guarrera's Worldsheet: Exotic R^4
		For example, a 2-sphere (the sphere you're used to) is homeomorphic to those Mickey Mouse ballons you can get at Disneyworld.
		The two sphere, however, would not be homeomorphic to the surface of a donut.
		This raises the possibility (at least to me), that you could define gauge theories (like the standard model) on exotic R^4's and perhaps get some physical effects that are not part of the standard model.
	web.mit.edu /guarrera/www/2005/10/exotic-r4.html (451 words)

	Exotic Classifieds
		In some states, it is illegal to keep exotics as pets.
		Exotic pets have different requirements, which can be both easy and difficult to meet.
		A smart diary is usually full of picture galleries and includes photographs on every sphere of the owner's life.
	www.bobcats-bobcats.com /bobcat-hunting/exotic-classifieds.html (186 words)

	The Black Hole Myth
		Physics is often a quest for the exotic truth.
		So we settle for the exotic that has little to do with the truth.
		Think of a fl hole being formed by a certain amount of mass M in the form of a fine dust (debris) collapsing due to gravity.
	www.engr.newpaltz.edu /~biswast/bhole/blackhole.shtml (2777 words)

	Maybe this Explains the Economic Cycle... best Exotic Sphere (Site not responding. Last check: 2007-11-01)
		Gromoll and Wolfgang Meyer, An exotic sphere with nonnegative sectional curvature, Ann...
		Exotic spheres as stationary sets of homotopy sphere involutions.
		In order to demonstrate that a smooth manifold M is an exotic sphere, there are clearly two...
	ascot.pl /th/Fourier3/Exotic-Sphere.htm (551 words)

	Paranormal News -- Your Source for UFO and Paranormal Related Information
		While we may not be able to fully describe the qualities of exotic spheres it seems quite possible that instead of radiating incoherent light as old Sol does the exotic sphere may be radiating more coherent energy waves.
		The responsive exotic energy system on our planet that couples with the drive from the exotic sphere would be the sinuous ’Dragon Line’ system so beloved of dowsers and geomantic specialists.
		Your local dragon line system is out of synch with the exotic sphere due to Doppler shift until you are traveling almost perfectly parallel to the surface of that sphere.
	www.paranormalnews.com /eyefriendly.asp?articleID=511 (7133 words)

	An exotic involution of the 5-sphere (Site not responding. Last check: 2007-11-01)
		The involution described in the movie is fixed point free since the axis of rotation in the second step is contained in the plane spanned by w and p.
		The exoticity of the involution is deduced from its origin: The Gromoll-Meyer sphere in dimension 7.
		Abresch, C. Duran, T. Püttmann, A. Rigas: Wiedersehen metrics and exotic involutions of Euclidean spheres, Preprint, December 2004.
	homepage.ruhr-uni-bochum.de /Thomas.Puettmann/XInvolution.html (247 words)

	Why not SEDENIONS?
		The 28 new associative triple cycles of the sedenions are related to the 28-dimensional Lie algebra Spin(0,8), and to the 28 different differentiable structures on the 7-sphere S7 that are used to construct exotic structures on differentiable manifolds.
		The Milnor spheres S(4k-1)#, of dimension 4k-1 for k=2 or greater, are homeomorphic to normal spheres S(4k-1) but not diffeomorphic to them.
		A 7-sphere, whether exotic S7# or normal S7, can be "factored" by a Hopf fibration into a 3-sphere S3 and a 4-sphere S4.
	www.valdostamuseum.org /hamsmith/sedenion.html (5107 words)

	Top Story - EXOTIC INNARDS OF A NEUTRON STAR REVEALED IN A SERIES OF EXPLOSIONS - November 06, 2002
		Neutron star EXO 0748-676 (blue sphere in Image 1) is part of a binary star system, and its neighboring star (yellow-red sphere in Image 1) supplies the fuel for the thermonuclear bursts.
		The neutron star is part of a binary star system named EXO 0748-676, located in the constellation Volans, or Flying Fish, about 30,000 light-years away in the Milky Way galaxy, visible in southern skies with a large backyard telescope.
		At such density, all the space is squeezed out of the atoms inside the neutron star, and protons and electrons squeeze into neutrons, leaving a neutron superfluid, a liquid that flows without friction.
	www.gsfc.nasa.gov /topstory/20021003nsexplosion.html (1055 words)

	Progress in Tapping Zero Point Energy for Space Exploration (Site not responding. Last check: 2007-11-01)
		Note that you need an anti-gravity repulsive core /\zpf of positive zero point energy density with negative quantum pressure to hold your EVO together because the electric repulsion energy is positive but decreases with increasing distance.
		The zero point energy induced strong gravity of the exotic vacuum core needs to be positive because it then increases with separation to make a minimum well of stability in the total potential energy!
		a uniform sphere of "dark matter" of radius r* like the Galactic Halo, assuming Hal's wrong PV model, then GM is replaced by -c^2/\zpfr^3 neglecting small rational factors of pi In the conventions used exotic* vacuum /\zpf < 0 gravitates as "dark matter" and /\zpf = 0 anti-gravitates as "dark energy".
	www.pych-one.com /new-5647113-4388.html (6186 words)

	Exotic Breeders (Site not responding. Last check: 2007-11-01)
		Many exotic breeders can provide you with photo galleries and separate photos of the animals available.
		The young and sick are the easiest to catch and when a caribou moves away from the herd the wolf pack chases it and surround.
		The calves are born with their eyes open and covered with warm fur.
	www.caribou-caribou.com /quebec-caribou-hunt/exotic-breeders.html (180 words)

	Physicists Clarify Exotic Force, But No 'Theory Of Everything' Yet
		When the sphere is brought near to the plate, an attractive Casimir force causes the cantilever to bend.
		To solve the problem, the team placed a tiny sphere made of gold on the tip of a flexible cantilever, giving the impression of a ball on the end of a diving board.
		A few hundred nanometers beneath the sphere was a plate made of two different materials — gold on one side, germanium on the other — both of which were then covered in a very thin layer of gold.
	www.spacedaily.com /news/physics-05y.html (1345 words)

	Re: multiple differentiable structures?
		So some exotic spheres are not so as "round" as you might think!
		I'm not sure exotic spheres are really relevant to physics, but it would be cool, so I'm glad some people are trying to establish connections.
		Kervaire and Milnor said the group of exotic spheres in dimension 9 was Z/2 x Z/2 x Z/2 or Z/2 x Z/4, and the group in dimension 17 was Z/2 x Z/2 x Z/2 x Z/2 or Z/2 x Z/2 x Z/4.
	www.lns.cornell.edu /spr/1999-12/msg0019934.html (2391 words)

	INTERFACE CONFIGURATION EXPERIMENT (USML-1) (Site not responding. Last check: 2007-11-01)
		Thus it is of great interest to determine experimentally what energy-mimimizing configurations there might be for the exotic containers, both as an indication of the limitations of classical theory and as a guide to future theoretical study.
		The infinite family of distinct symmetric equilibrium interfaces that are possible for the exotic container bulges cannot form.
		The results of this test will be valuable as a control to compare with the behavior in the exotic containers, and for obtaining information about the effects on surface reorientation of resistance at the contact line and presence of the (reentrant) corner between the bulge and cylindrical portions of the containers.
	exploration.grc.nasa.gov /expr2/ice.htm (1966 words)

	[No title]
		He first ex- plained to me why every element in the homotopy groups of spheres is a `higher * order Toda bracket' of Adams filtration one elements; this is now a main ingredient of the inductive a *rgument in Lemma 4.1.
		Since F(Sn+1(p)) is an (n+1)-dimensional p-local sphere, the lift of ff fact* *ors through the (n+1)-dimensional ___ skeleton_of the spectrum HZ (p).
		With this convention we have to show that the Hopf maps j; and oe are in the image of F in dimensio* *ns 1, 3 and 7 respectively.
	hopf.math.purdue.edu /Schwede/2local.txt (3287 words)

	Encyclopedia of Laser Physics and Technology - laser cavities, laser diodes, laser design, linewidth, laser safety, ...
		A laser requires a laser cavity (or laser resonator), in which the laser radiation can circulate and pass a gain medium which compensates the cavity losses.
		Exceptions are only exotic cases where a medium with very high gain is used, so that amplified spontaneous emission extracts significant power in a single pass through the gain medium.
		When calculating light forces on atoms, it is often more convenient to derive the light forces from the gradient of a potential which arises from the interaction of the atoms with the light field.
	www.rp-photonics.com /encyclopedia_l.html (6940 words)

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