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Topic: List of geometric topology topics

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	Topology - Wikipedia, the free encyclopedia
		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).
		Internally to the subject, elementary topology is often called point-set topology or general topology, to distinguish it from more advanced areas such as algebraic topology (which grew out of combinatorial topology), geometric topology and low-dimensional topology dealing for example with knot theory, and differential topology.
		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 (1548 words)

	Geometric topology - Wikipedia, the free encyclopedia
		In mathematics, geometric topology is the study of manifolds and their embeddings, with representative topics being knot theory and braid groups.
		In the rapid development of topology after 1945, a distinction was drawn between the fields of algebraic topology typified by homotopy theory, geometric topology with the Poincaré conjecture as its biggest unsolved problem, and differential topology as the study mostly of differential structures, with Morse theory as its natural technique.
		Thurston's geometrization conjecture, formulated in the late 1970s, offered a framework that suggested geometry and topology were closely intertwined in low dimensions, and Thurston's proof of geometrization for Haken manifolds utilized a variety of tools from previously only weakly linked areas of mathematics.
	www.wikipedia.org /wiki/Low-dimensional_topology (300 words)

	[No title]
		In architecture, topology is a term used to describe spatial effects which can not be described by topography, i.e., social, economical, spatial or phenomenological interactions.
		In mathematics, topology is a branch concerned with the study of topological spaces.
		Johann Benedict Listing (1808-1882) in "Vorstudien zur Topologie," Vandenhoeck und Ruprecht, Göttingen, pp.
	en-cyclopedia.com /wiki/Topology (1239 words)

	Topology (Site not responding. Last check: 2007-10-18)
		In mathematics, topology is a branch concerned with thestudy of topological spaces.
		Topology is also concerned with the study of the so-called topological properties of figures, that is to say properties thatdo not change under bicontinuous one-to-one transformations (called homeomorphisms).
		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 onarbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomologytheories.
	www.therfcc.org /topology-89.html (1256 words)

	Encyclopedia: Geometric topology (Site not responding. Last check: 2007-10-18)
		The methods of geometric topology being combinatorial, and difficulties arising (for example in Dehn's lemma), the field was something of a poor relation.
		The solution by Smale of the Poincaré conjecture in higher dimensions changed matters somewhat, in that it made dimensions three and four seem the hardest; and indeed they required new methods, while the freedom of higher dimensions meant that questions could be reduced to computational methods available in surgery theory.
		A number of advances, on the Poincaré conjecture and the geometrization conjecture programme, and on knot invariants such as new knot polynomials, had the effect of changing geometric topology.
	www.nationmaster.com /encyclopedia/Geometric-topology (299 words)

	Miscy Directory - Top > Science > Math > Topology (Site not responding. Last check: 2007-10-18)
		Topics in Mathematics - Topology - In the Mathematics Archives at University of Tennessee, Knoxville.
		Topology of Manifolds: Supersymmetry and QFT - This is the web resource page for a course taught by John Morgan in Fall 1997 at Columbia University.
		Algebraic Topology Discussion List - The primary functions of this list are: providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology.
	dir.miscy.com /Science/Math/Topology (283 words)

	Directory - Science: Math: Topology
		Topics in Mathematics - Topology · cached · In the Mathematics Archives at University of Tennessee, Knoxville.
		Algebraic Topology Discussion List · cached · The primary functions of this list are: providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology.
		Topology of Manifolds: Supersymmetry and QFT · cached · This is the web resource page for a course taught by John Morgan in Fall 1997 at Columbia University.
	www.incywincy.com /default?p=26919 (254 words)

	Gourt :: Science :: Math :: Topology
		Algebraic Topology Discussion List: The primary functions of this list are: providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology.
		Topics in Mathematics - Topology: In the Mathematics Archives at University of Tennessee, Knoxville.
		Topology of Manifolds: Supersymmetry and QFT: This is the web resource page for a course taught by John Morgan in Fall 1997 at Columbia University.
	science.gourt.com /Math/Topology.html (325 words)

	Topology (Site not responding. Last check: 2007-10-18)
		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).
		Two figures that can be deformed one into the other are called homeomorphic, and are considered to be the same from the topological point of view.
	www.usedaudiparts.com /search.php?title=Topology (1315 words)

	Read about Category:Topic lists at WorldVillage Encyclopedia. Research Category:Topic lists and learn about ... (Site not responding. Last check: 2007-10-18)
		Lists of articles by category for a structured list and overview.
		List of formal language and literal string topics
		List of harmonic analysis and representation theory topics
	encyclopedia.worldvillage.com /s/b/Category:Topic_lists (118 words)

	Allen Hatcher's Homepage
		This is the first in a series of three textbooks in algebraic topology having the goal of covering all the basics while remaining readable by newcomers seeing the subject for the first time.
		The idea would be to present an introduction to differential topology that goes as far as developing the theory of exotic spheres, that is, nonstandard differential structures on the standard topological sphere.
		Geometrically, the picture involves the hyperbolic plane and its isometries.
	www.math.cornell.edu /~hatcher (1123 words)

	Topology - InfoSearchPoint.com (Site not responding. Last check: 2007-10-18)
		(The term topology is also used for a set of open sets used to define topological spaces, but this article focuses on the branch of mathematics.
		Wiring and computer network topologies are discussed in network topology.) Roughly speaking, topology is the study of geometric objects without considering their dimensions.
		Leonhard Euler's paper on Seven Bridges of Königsberg is regarded as one of the first result on geometry that does not depend on any measurements, i.e., on topology.
	www.infosearchpoint.com /display/Topology (1125 words)

	LIST OF ARTICLES BY CATEGORY (Site not responding. Last check: 2007-10-18)
		None of these are yet comprehensive or up-to-date, but filling in or creating these lists will create an easy way to track articles by their categories, as well as creating an implicit to-do list of topics for which articles have not yet been written.
		List of astronomical topics, expanded list of topics from N-Z
		List of anomalous phenomenon (paranormal) and parapsychology topics
	www.websters-online-dictionary.org /definition/LIST+OF+ARTICLES+BY+CATEGORY (307 words)

	Geometric topology -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-18)
		These fields all rested on (Click link for more info and facts about general topology) general topology, which was the study of the general ((mathematics) any set of points that satisfy a set of postulates of some kind) topological space.
		The solution by (Click link for more info and facts about Smale) Smale, in 1961, of the Poincaré conjecture in higher dimensions made dimensions three and four seem the hardest; and indeed they required new methods, while the freedom of higher dimensions meant that questions could be reduced to computational methods available in surgery theory.
		See also: (Click link for more info and facts about list of geometric topology topics) list of geometric topology topics
	www.absoluteastronomy.com /encyclopedia/g/ge/geometric_topology.htm (241 words)

	List of lists of mathematical topics - Bvio (Site not responding. Last check: 2007-10-18)
		List of lists of mathematical topics - Bvio
		List of terms relating to algorithms and data structures
		List of theorems -- see also list of mathematical theorems.
	bvio.ngic.re.kr /Bvio/index.php/List_of_mathematical_topics_%28lists%29 (94 words)

	Amazon.com: A Geometric Introduction to Topology: Books (Site not responding. Last check: 2007-10-18)
		It is unique in not presupposing a course in general topology and in avoiding the use of simplexes.
		This discussion introduces the important concept of the degree of a map, and this is used to prove the fundamental theorem of algebra and the Brouwer fixed point theorem in the plane.
		This is a fundamental result in algebraic topology, and the author computes the first singular cohomology group of a product as an example of this result.
	www.amazon.com /exec/obidos/ASIN/0486678504/ref (828 words)

	Courses in mathematics (Site not responding. Last check: 2007-10-18)
		Topics include the definite integral, techniques of integration, and applications of the integral.
		Topics include functions of more than one variable: partial and total derivatives, multiple integrals, vector-valued functions, parametrized curves, and applications to differential equations.
		Topics will include Partial Differential Equations (heat equation, wave equation, eigenfunction expansions, qualitative properties) and Linear Programming (simplex algorithm, duality theory, applications in operations research, game theory) or Chaos and Fractals (one- and two-dimensional discrete dynamics, iterated functions, fractal dimension).
	www.cs.grinnell.edu /catalog/math-courses.xhtml (864 words)

	The Math Forum - Math Library - Topology (Site not responding. Last check: 2007-10-18)
		A multi-purpose center for electronic distribution of information related to topology, the mathematical study of surfaces, sometimes called "rubber sheet geometry" because topologists consider geometric figures as though they were drawn on infinitely stretchable rubber sheets.
		An list of suggestions for projects in geometry, topology, symmetry, making geometric solids, calendars, spherical and hyperbolic trigonometry, puzzles, models, etc. Projects were to be exhibited at the Geometry Fair at the end of the course.
		A refereed archive of interesting geometric examples and visualizations, open for any geometer to publish new geometric models, or to browse the models for material to be used in education and research.
	forum.swarthmore.edu /library/topics/topology (2430 words)

	Amazon.com: Topology: Books (Site not responding. Last check: 2007-10-18)
		Many students have been educated in topology by using this book, and it is sure to remain a classic in the field.
		These strategies have varying degrees of success, but their use in topology now seems to be reaching a saturation limit, even though the explicit calculation of homotopy groups is still a very active area.
		An excellent book, not for those persons unfamiliar with the topic of topolgy; yet, combined with simpler texts this book is a goldmine of topological theorems and their proofs.
	www.amazon.com /exec/obidos/tg/detail/-/0486656764?v=glance (1319 words)

	The Mobius band (from topology) -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-18)
		More results on "The Mobius band (from topology)" when you join.
		Provides information on algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g.
		Contains comprehensive listings of preprints, abstracts, contributions, journals, periodicals, educational articles, FAQs, conferences, and employment opportunities.
	www.britannica.com /eb/article-69097 (900 words)

	57: Manifolds and cell complexes
		These types of spaces admit very precise answers to questions about existence of maps and embeddings; they are particularly amenable to calculations in algebraic topology; they allow a careful distinction of various notions of equivalence.
		General topology is for spaces without the local Euclidean nature of the spaces in this section.
		Geometric topology is a natural language in which to study families of motions; applications include some topics in mechanics of moving particles and systems.
	www.math.niu.edu /~rusin/known-math/index/57-XX.html (768 words)

	Geometric Topology Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-18)
		Looking For geometric topology - Find geometric topology and more at Lycos Search.
		Find geometric topology - Your relevant result is a click away!
		Look for geometric topology - Find geometric topology at one of the best sites the Internet has to offer!
	www.karr.net /search/encyclopedia/Geometric_topology (468 words)

	Math 434. Geometric Topology (Site not responding. Last check: 2007-10-18)
		The first few weeks of the semester will cover most of Hatcher's Notes on Basic 3-Manifold Topology, covering examples of 3-manifolds, Kneser's prime decomposition theorem, JSJ decomposition, loop and sphere theorems.
		Topics for presentations include, but aren't limited to, this list.
		A nice paper by George Francis and Jeff Weeks that explains Conway's ZIP proof (of the fundamental theorem of compact surfaces).
	www.math.uiuc.edu /~brinkman/teaching/math434 (119 words)

	OUP: Geometric Topology: Kazez
		This is a two-part volume reflecting the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August.
		Kirby's problem list, which contains a thorough description of the progress made on each of the problems and includes a very complete bibliography, makes the work usefyl for specialists and non-specialists who want to learn about the progress made in many areas of topology.
		Gabai's problem list, which focuses on foliations and laminations of 3-manifolds, collects for the first time in one paper definitions, results, and problems that may serve as a defining source in the subject area.
	www.oup.co.uk /isbn/0-8218-0652-1 (340 words)

	Math > Topology > General Topology at b2bYellowpages.com Subject Directory (Site not responding. Last check: 2007-10-18)
		Oxford Analytic Topology Research Group - Research interests: topology of metric spaces, generalised metric spaces, continua, function spaces, hyperspaces, topological algebra, set theoretic methods in topology, and applications of topology to computer science and the theory of differential equations.
		Textbook in Problems on Elementary Topology - The core of the book is the material included usually into the Topology part of the two year geometry course in the Mathematical Department of St. Petersburg University.
		Topology - Descriptions and illustrations of several Topological and Differential Geometry related notions.
	www.b2byellowpages.com /web.cgi/Science/Math/Topology/General_Topology (557 words)

	Future Research Topics
		Quillen's geometric interpretation of cobordism: cobordism is traditionally viewed as a relation on manifolds of finite dimension and usually applied to compact manifolds.
		This topic would be very geometric and probably requires a study of the analysis of maps between infinite dimensional manifolds as well as `classical' cobordism theory.
		There are other interesting geometric questions about even the finite dimensional theory that appear not to have been studied and these would also provide a good area to work on.
	www.maths.gla.ac.uk /~ajb/andy-research.html (968 words)

	Conference in Goemetric Topology
		In conjunction with the next International Congress of Mathematicians (Beijing, 8/20--28, 2002), we are organizing a week-long Conference in Geometric Topology as one of its satellite conferences.
		This Conference in Geometric Topology is aimed at reflecting the current state of the art in the study of low dimensional topology and related subjects.
		The specific range of topics we intend to cover is well represented by the interests of the members of the advisory committee.
	www.math.uiowa.edu /~wu/gtc/gtc.html (273 words)

	Geometric Topology Research Focus Group (Site not responding. Last check: 2007-10-18)
		This will be the main site for coordinating the Geometric Topology Research Focus Group activities in 2002-2003.
		Topics are prime and toral decomposition theorems, more on Seifert manifolds, torus bundles and semibundles, and loop and sphere theorem and Dehn's lemma.
		A good collection of problems in low dimensional topology can be found at Rob Kirby's web page.
	www.math.ucdavis.edu /~hass/TopologyRFG/topologyRFG.html (198 words)

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