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Topic: Topology of the universe

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	Shape of the universe - Wikipedia, the free encyclopedia
		Cosmologists and astronomers describe the geometry of the observable universe which includes both local geometry and global geometry of the whole universe, which is in practice loosely termed topology, even though strictly speaking it goes beyond topology.
		The shape of the universe is not concerned with a geometry near to a dense mass.
		Notwithstanding that the universe is "weakly" inhomogeneous and anisotropic in the large-scale structure of the cosmos, both astronomical and cosmological measurements determine the observable universe to be, on average, homogeneous, isotropic, and expanding or accelerating.
	en.wikipedia.org /wiki/Topology_of_the_universe (1303 words)

	Topology - Wikipedia, the free encyclopedia
		Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants.
		Topology has sometimes been called rubber-sheet geometry, because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without tearing).
		In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories.
	en.wikipedia.org /wiki/Topology (1533 words)

	Topology
		Cone (topology) In quotient The cone is used in algebraic topology precisely because it embeds a space as a subspace of...
		Glossary of differential geometry and topology This is a differential topology.
		Topology glossary This is a glossary of some terms used in the branch of general topology and on definitions that are fu...
	www.brainyencyclopedia.com /topics/topology.html (737 words)

	Encyclopedia: Topology
		Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces.
		Topology is concerned with the study of the so-called topological properties of figures, that is to say, properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms).
		In the mathematical field of topology a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms.
	www.nationmaster.com /encyclopedia/Topology (4573 words)

	Topology of the Universe (Site not responding. Last check: 2007-11-07)
		In a the context of physics, General relativity relates the distribution of mass in the universe to its geometry and the geometry of the universe determines the dynamics of the mass.
		Topology is a global quantity that characterizes the shape of space (Measuring the Topology of the Universe, Cornish, Spergel, and Starkman).
		Unlike the geometry of the universe, the topology of the universe is not constrained by General Relativity.
	astro.uchicago.edu /home/web/olinto/courses/A18200/nbower.htm (1757 words)

	Cosmology and Topology
		The universe does not have a structure of immutable Euclidean space woven by an independent time; it is described as a space-time distorted by the presence of matter and energy.
		As a manifestation of the curvature of space-time, gravitation dictates the trajectories of particles and light rays, compelled to marry contours of a non-Euclidean four-dimensional geometry.
		Topology is the branch of geometry which classifies spaces according to their global shape.
	luth2.obspm.fr /~luminet/etopo.html (3625 words)

	Nat' Academies Press, (NAS Colloquium) The Age of the Universe, Dark Matter, and Structure Formation (1998)
		Our interest in the topology of the universe was stimulated by the possibility that it may be detectable and by the philosophical attractions of a finite universe (21).
		General relativity relates the mass distribution of the universe to its geometry, and, of course, the geometry of the universe determines the dynamics of the mass.
		Topology is a global quantity that characterizes the shape of space (see, e.g., ref. 25 for a general introduction).
	www.nap.edu /books/0309060265/html/82.html (3838 words)

	Topology -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Topology is concerned with the study of the so-called (Click link for more info and facts about topological properties) topological properties of figures, that is to say properties that do not change under bicontinuous one-to-one transformations (called (Click link for more info and facts about homeomorphism) homeomorphisms).
		One of the first papers in topology was the demonstration, by Leonhard Euler, that it was impossible to find a route through the town of Königsberg (now (Click link for more info and facts about Kaliningrad) Kaliningrad) that would cross each of its seven bridges exactly once.
		Every closed (The difference in pitch between two notes) interval in R of finite length is (A small cosmetics case with a mirror; to be carried in a woman's purse) compact.
	www.absoluteastronomy.com /encyclopedia/t/to/topology.htm (1920 words)

	sciforums.com - What causes the universe to be hyperbolic?
		The universe may have any type of topography, what we can be sure of, after the map results, is that it is open.
		This is extraordinary because as the Universe expands the density parameter should move away from the critical value.
		Most of the helium in the universe was created from the primordial neutrons and protons (Although stars do produce some of the helium visible today), by the time the ucleosynthesis epoch ended.
	www.sciforums.com /showthread.php?t=17623 (1081 words)

	National Institute for Discovery Science: Topology of the Universe
		The most basic idea behind the topology of the universe is whether the universe has positive, negative, or zero curvature, i.e., whether it is closed, open, or flat.
		The topology of a doughnut is neither flat nor closed in a positive sense, and is also different from an infinite open saddle in the sense that if you traveled far enough in any one direction along the surface of the doughnut, you'd arrive back at where you had started.
		There are many topologies of a compact hyperbolic universe which have effects at angular scales which could be detected by MAP or Planck (in fact, there are infinitely many of these topologies).
	www.nidsci.org /articles/universe_topology.php (528 words)

	SPACE-TALK - The Universe's Topology...
		It is difficult to imagine that the universe resides on the surface of a fourth dimensional torus (or any other multiply connected surface) because, if it did, then a 3 dimensional curve drawn on its surface would not be able to contract to a single point.
		However, if the universe were a multiply connected surface, then it would be possible to orient a sphere on the surface of the universe that could not be contracted to a point - that is, if the universe, itself, were not contracted to a point.
		The consequence of this is that in such a universe, if there was a spherical mass which was sufficiently large and oriented properly, then it could not be contracted to a point and remain in the universe.
	www.space-talk.com /ForumE/showthread.php3?threadid=1501 (702 words)

	Open Questions: Large-scale Structure of the Universe
		A brief tutorial on possible topologies of the universe, and evidence from studies of the cosmic microwave background that constrain the possibilities, by Angelica de Oliveira-Costa.
		It depends on the topology of spacetime, and observations of the cosmic background radiation that will be feasible in just a few years should make it possible to determine the topology.
		The idea is that if the universe is finite (necessary if the overall curvature is positive, but still possible even if the curvature is zero or negative), temperature fluctuations in the CMB will repeat in a predictable way that reveals the topology.
	www.openquestions.com /oq-co006.htm (947 words)

	Spherical Universe
		As a consequence, cosmic topology has gained an increased interest, as evidenced by the special session "Geometry and Topology of the Universe" organized by the American Mathematical Society during its 2001 meeting held last October in Williamstown, Mass.
		The researchers have particularly studied small universe models, which explain the billions of visible galaxies are repeating images of a smaller number of actual galaxies.
		In a multi-connected Universe, the physical space is identified to a fundamental polyhedron, the duplicate images of which form the observable universe.
	www.obspm.fr /actual/nouvelle/dec01/luminet.en.shtml (953 words)

	Geometry of the Universe
		All types of topologies are possible such as spherical universes, cyclindrical universes, cubical universes with opposited edges identified or more complicated permutations of the identifications including twists and inversions or not opposite sides.
		It could be that the topology of the Universe is very complicated if quantum gravity and tunneling were important in the early epochs.
		The usual assumption is that the universe is, like a plane, "simply connected," which means there is only one direct path for light to travel from a source to an observer.
	zebu.uoregon.edu /~js/cosmo/lectures/lec15.html (1125 words)

	Topology of the Universe: Background and recent \\ observational approaches (Site not responding. Last check: 2007-11-07)
		Topology of the Universe: Background and recent observational approaches
		A flat or hyperbolic (`open') FL universe is not necessarily infinite in volume.
		The methods of detecting multiply connected models (MCM's) are presently in their pioneering phase of development and the optimal observationally realistic strategy is probably yet to be calculated.
	www.ias.ac.in /pramana/v53/p945/abs.htm (210 words)

	Bob Gardner's "Topology, Cosmology and Shape of Space" Talk, Section 7 (Site not responding. Last check: 2007-11-07)
		Some 200,000 years after the big bang, the universe became transparent to radiation and a shower of light was released.
		In such a case, we could detect the topology of the universe by looking for these circles in the sky.
		For example, if the universe is a giant 3-torus, then we might see three pairs of circles in the sky, each resulting from the intersection of the CMB sphere with itself in the principle directions (the front-back, left-right, and top-bottom as described above).
	www.etsu.edu /physics/etsuobs/starprty/120598bg/section7.htm (388 words)

	► » Topology of the universe (Site not responding. Last check: 2007-11-07)
		universe forever expanding under the pressure of dark energy.
		Big Bang would fill the universe on all length scales.
		Cosmology: The shape of the Universe p 566
	www.science-one.org /Topology-of-the-universe-3479677.html (545 words)

	Science News Online (2/21/98): Circles in the Sky Detecting the shape of the universe by Ivars Peterson
		Among the startling possibilities are those corresponding to a finite universe, in which a starship could blast off on a voyage of a few billion light-years in one direction and eventually return from another direction.
		Prompted in part by the enticing possibility of detecting the signature of the universe's topology in detailed maps of temperature fluctuations throughout space, a group of scientists and mathematicians met last October at Case Western Reserve University in Cleveland to compare notes.
		Knowing the topology, researchers could independently determine the ratio of the universe's density to its critical value and reconstruct the state of the universe that gave rise to the cosmic microwave background.
	www.sciencenews.org /sn_arc98/2_21_98/bob1.htm (1917 words)

	Love on the edge of the universe (July 2002) - Review - PhysicsWeb (Site not responding. Last check: 2007-11-07)
		One of just two people at the 100-strong conference trying to determine the topology of the universe, Levin stole the show with her natural talent for presentation and the quality of her material.
		In particular, it cannot say whether the universe has any holes in it, or if a light ray sent from a point could travel all the way round the universe to return to where it was emitted.
		Testing the shape of the universe is made all the more difficult by the fact that we cannot step outside of it, by moving up a dimension and peering down on the universe to look for evidence of finiteness.
	physicsweb.org /articles/review/15/7/1 (1408 words)

	Topology_of_the_universe
		Notwithstanding that the universe is "weakly" inhomogeneous and anisotropic in the large-scale structure of the cosmos, both astronomical and cosmological measurements determine the observable universe to be, on average, homogeneous, isotropic and an expanding, or accelerating, universe.
		Expressing the ratio of average energy density of the universe over critical energy density as Ω, the curvature is given as:
		If the geometry of the universe is not compact, then it is infinite in extent with infinite paths of constant direction that, generally do not return and the space has no definable volume and an arbitrary scale, such as the Euclidean plane.
	www.freecaviar.com /search.php?title=Topology_of_the_universe (1342 words)

	Biology News: Sizing up the Universe
		A recent suggestion that the cosmos could be shaped like a soccer ball1, for example, would have meant that the universe was just 60 billion light years across.
		If the universe were relatively small, it would not necessarily be that obvious because it would not have to have an edge.
		He concludes that the universe must be larger than 78 billion light years across, much larger than the 28 billion light years or so that we can see with our telescopes.
	www.bioedonline.org /news/news.cfm?art=977 (610 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		We propose a simple possible topological explanation of why charge is quantized, involving a tiny permanent magnetic field trapped in the topology of the universe.
		The idea apparently works for every possible compact 3-manifold topology for the universe except for ``rational homology spheres.'' This picture does not need to assume magnetic monopoles exist, and indeed looks incompatible with their existence.
		We present an argument that all orientable 3-manifolds should be consistent with a very wide class of possible laws of physics; but almost all $n$-manifolds for almost all $n \ne 3$ won't be.
	www.math.temple.edu /~wds/homepage/chargequant2.sue (281 words)

	New Scientist Breaking News - Big Bang glow hints at funnel-shaped Universe
		It may sound like a surrealist's dream, but according to Frank Steiner at the University of Ulm in Germany, recent observations hint that the cosmos is stretched out into a long funnel, with a narrow tube at one end flaring out into a bell.
		Back when the Universe was only 380,000 years old it would have been a fraction of that size, too small to allow big fluctuations.
		In the flat space of conventional cosmology, the smallest blobs on microwave sky maps ought to be round.
	www.newscientist.com /article.ns?id=dn4879 (780 words)

	Geometry of Universe (Site not responding. Last check: 2007-11-07)
		However, in the context of plausible models, which can be tested, one can measure directly the curvature of space though the angular location of the "acoustic peaks" in the CMB anisotropy power spectrum.
		Preliminary results at this time show that the curvature of the Universe is small and consistent with a "flat" = Euclidean geometry.
		This means for example that the Universe has rotated less than one second of arc in the last 10 billion years.
	aether.lbl.gov /www/science/geometry.html (342 words)

	OSU Physics: Calendar of Events
		Description: Recent satellite data are beginning to reveal the curvature and topology of the universe.
		We'll see how measurements of the cosmic microwave background radiation are determining the curvature of the universe to unprecedented precision.
		The second half of the presentation will use computer games to introduce the concept of a finite, multiconnected universe, and we'll see how the same satellite data suggest the real universe may be multiconnected.
	www.physics.ohio-state.edu /calendar/event.php3?id=604 (175 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Glenn Starkman Case Western Circles in the Sky: Determining the Universe's Topology with the Microwave Background Radiation If $\Omega<1$, and the universe is negatively curved, topology on scales significantly smaller than the horizon is expected and not ruled out.
		Previous contraints on topology were specific to flat space, $\Omega=1$, and do not apply to negatively-curved space.
		If the universe is topologically interesting then generically the signature of the topology of the universe is writ clearly on the cosmic microwave background sky.
	www.ifa.hawaii.edu /colloquia/abstracts/starkman.txt (131 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The global topology of the universe is as testable an attribute as the curvature and will leave a fossil record in the microwave sky.
		If the universe is finite and multiconnected, then only fluctuations which could fit inside the compact space are allowed.
		One possible topology is that the universe has negative curvature but is not infinite.
	cosmology.berkeley.edu /dir/janna/maps.html (484 words)

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