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Topic: Geometric topology

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	Topology
		Topology is the mathematical study of those properties that are preserved through continuous deformations of objects.
		A circle is topologically equivalent to an ellipse, a sphere is equivalent to a cube, and a coffee cup to a donut.
		Geometric topology is the study of manifolds and their embeddings, with representative topics being knot theory and braid groups.
	www.math.neu.edu:16080 /research/topology.html (257 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 and transversality as their natural techniques.
		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.
	en.wikipedia.org /wiki/Geometric_topology (356 words)

	People Topology Math Science
		Geometric Group Theory and Low-Dimensional Topology, as well as the neighboring fields of Combinatorics, Graph theory, Computational Geometry and certain types of Riemannian Geometry.
		With textbooks on Algebraic Topology, Vector Bundles and K-theory, and 3-manifolds.
		Topology and combinatorics: hyperplane arrangements, the topology and geometry of manifolds, the homology of discrete groups, the homotopy theory of high-dimensional knots.
	www.iaswww.com /ODP/Science/Math/Topology/People (441 words)

	The Univ. of Iowa, Topology Group
		His interests are in the topology of varieties and singularites, arrangements of hyperplanes, and piecewise-linear knot theory.
		His interests are in the area of geometric topology, especially in dimensions that are small but more than 3, such as knotted surfaces in 4-space and knot energies for these.
		His research interests are in the area of geometric topology and low-dimensional manifolds ; in particular, 3-manifolds and knot theory.
	www.math.uiowa.edu /faculty/researchGroups/topology.htm (270 words)

	Topology: A Geometric Approach American Mathematical Monthly, The - Find Articles (Site not responding. Last check: 2007-10-13)
		In some circles, basic undergraduate point-set topology is going the way of analytic geometry: you're supposed to know it, but it doesn't get taught regularly.
		Topology, defined as the study of mathematical phenomena that remain invariant under continuous (i.e., not necessarily linear, or differentiable, or distance preserving) deformations, is a very fundamental sort of geometry, and for that reason alone we should be studying it.
		One of our basic geometric facts is that any connected, compact, orientable surface is homeomorphic to a g-holed torus and that a g-holed torus and an h-holed torus are homeomorphic if and only if g = h.
	www.findarticles.com /p/articles/mi_qa3742/is_200604/ai_n16123368 (930 words)

	What is topology?
		Moreover, geometric concepts such as slopes of lines and areas of regions can usefully be interpreted in terms of thermodynamics.
		Where geometrical concepts are used, they must be defined in terms of algebraic ones.
		All use of such concepts is to be justified purely in terms of such definitions, rather than in terms of geometric intuition.
	www.shef.ac.uk /~pm1nps/Wurble.html (1402 words)

	Crystallographic Topology 101 - Overview
		For our purpose we will say that crystallography is the study of atoms in crystals, topology is the study of distortion-invariant connectivity properties of mathematical objects, and crystallographic topology is an intersection of those two disciplines.
		Since both topology and crystallography have many subdisciplines, there are a number of quite different intersection regions that can be called crystallographic topology; but we will confine this discussion to one small, well delineated subarea.
		The geometric topology of interest is the topological properties of crystallographic groups, represented as orbifolds, and the Morse theory global analysis of critical points in symmetric functions.
	www.ornl.gov /ortep/topology/overview.html (2580 words)

	Salvador Vera: Directorio - Topología (Site not responding. Last check: 2007-10-13)
		Topology of Manifolds: Supersymmetry and QFT This is the web resource page for Topology of Manifolds, taught by John Morgan in Fall 1997 at Columbia University.
		Geometry and Topology A fully refereed international journal dealing with all aspects of geometry and topology and their applications.
		Research interests are in geometric topology and the theory of low-dimensional manifolds: particularly knot theory, polynomial invariants of links, and quantum invariants of 3-manifolds derived, via skein theory, from link invariants.
	www.satd.uma.es /matap/svera/links/matnet15.html (626 words)

	The Math Forum - Math Library - Topology (Site not responding. Last check: 2007-10-13)
		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.
	mathforum.org /library/topics/topology (2425 words)

	Topology and its Applications (Site not responding. Last check: 2007-10-13)
		Topology and its Applications is a research journal devoted to many areas of topology, and is published by Elsevier Science B.V. in Amsterdam.
		The mathematical focus of the journal will be that suggested by the title, research in topology.
		It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal.
	www.math.ucsb.edu /~long/TAIA/TopApp.htm (702 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.
		This is intended to be a readable introduction to spectral sequences, with emphasis on their applications to algebraic topology.
		The little that exists of the 3-manifolds book is rather crude and unpolished, and doesn't cover a lot of material, but it does contain a few things that aren't readily available elsewhere, like the elementary form of the Jaco-Shalen/Johannson torus decomposition theorem.
	www.math.cornell.edu /~hatcher (875 words)

	DaVinci: Science> Math> Topology
		Ghrist is an expert at applying a branch of mathematics called topology to...
		Math professor Marina Ratner, who taught Fire in a graduate-level general topology class when Fire was in his sophomore year, described him as "brilliant." She...
		She is a mathematician trying to get a handle on the topology of our universe, which...
	www.bluegrassdavinci.com /ODP/Science/Math/Topology (488 words)

	Wiley::Topology and Its Applications (Site not responding. Last check: 2007-10-13)
		It is designed for use either for a first course in topology beginning in chapter one, a first course in geometric topology beginning in chapter three or a course in applied topology.
		The book is structured around the theoretical framework of topology, and abundant illustrations and applications provide intuition and put the subject in modern setting.
		In this text serious attention is given to recent applications of topology in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, population modeling and other areas of science and engineering.
	www.wiley.com /WileyCDA/WileyTitle/productCd-0471687553.html (226 words)

	Scrooble.com for : Geometric Topology
		The common misspelling of the word geometric topology are shown below.
		A professor of mathematics at Lafayette College, Meier’s primary research focuses on geometric group theory and topology.
		Topology, topography, shape and size optimization capabilities are now available with...
	www.scrooble.com /mathematics/geometric-topology.htm (84 words)

	Basic Library List-Topology
		Fuks, D.B. and Rokhlin, V.A. Beginner's Course in Topology: Geometric Chapters New York, NY: Springer-Verlag, 1984.
		From Geometry to Topology Philadelphia, PA: Crane, Russak, 1974.
		Moise, Edwin E. Geometric Topology in Dimensions 2 and 3 New York, NY: Springer-Verlag, 1977.
	www.maa.org /BLL/topology.htm (866 words)

	GEOMETRIC TOPOLOGY II
		Shape Theory and Geometric Topology, 1981 (Lecture Notes in Mathematics #870, Springer, Berlin 1981) (Participants)
		Geometric Topology and Shape Theory, 1986 (Lecture Notes in Mathematics #1283, Springer, Berlin 1987) (Participants)
		Geometric Topology, 1998 (Topology and Its Applications, Vol.
	web.math.hr /~ungar/Dubrovnik2002 (62 words)

	Omniseek: /Science & Tech /Math /Topology /Geometric Topology
		According to Webster's New Universal Unabridged Dictionary (Deluxe Second Edition), topology is: "The study of those properties of geometric figures that remain unchanged even when under distortion, so long as no surfaces are torn."
		is informally classified into several subdisciplines according to the types of methods brought to bear on topological problems: set theoretic topology; geometric and differential topology;...
		Proceedings of 1996 Josai Conference on Surgery and Geometric Topology
	www.omniseek.com /srch/{48290} (404 words)

	Links to low-dimensional topology: Conference Announcements
		The Midwest Topology Seminar is held three times each year, usually in the Chicago area.
		The meeting in Storrs, CT, October 28-29, 2006, includes an in vited talk by Katrin Wehrheim, and special sessions on Combinatorial Methods in Equivariant Topology, Geometric Structures Related to Quantum Field Theory, Teichmuller Theory and Hyperbolic Geometry, and Topology and Computing.
		A conference on Geometric and Topological Aspects of Group Theory held at MSRI, May 8-12, 2000.
	www.math.unl.edu /~mbrittenham2/ldt/conf.html (882 words)

	Geometric Topology at UW-Milwaukee (Site not responding. Last check: 2007-10-13)
		The Geometric Topology group at the University of Wisconsin-Milwaukee is small but very active.
		For students specializing in topology we have recently offered advanced courses on a variety of topics, including: differential topology, dimension theory, topological manifolds and polyhedra, surgery theory, and geometric group theory.
		Okun is a recent addition to the UWM topology group, arriving in the fall of 2001.
	www.uwm.edu /~craigg/geotop.html (335 words)

	Topology in Matsue 2002 --Top--
		Shimane University and the Mathematical Society of Japan are organizing the international conference "Topology in Matsue".
		General Topology, Geometric Topology, Homotopy Theory, Knot Theory, Set-Theoretic Topology, Set theory and Applications.
		The session of General and Set-Theoretic Topology will be dedicated to Professor Jun-iti Nagata on his 77th birthday.
	www.math.shimane-u.ac.jp /~top2002 (286 words)

	Publications of Stavros Garoufalidis. (Site not responding. Last check: 2007-10-13)
		S. and Y. Lan, Experimental evidence for the Volume Conjecture of the simplest hyperbolic non-2-bridge knot, Algebraic and Geometric Topology, 5 (2005) 379--403.
		N. Dunfield and S. Nontriviality of the A-polynomial for knots in S^3, Algebraic and Geometric Topology, 4 (2004) 1145-1153.
		S. On the characteristic and deformation varieties of a knot, Proceedings of the Casson Fest, Geometry and Topology Monographs, 7 (2004) 291-309.
	www.math.gatech.edu /~stavros/publications/publications.html (849 words)

	Topology 1 -- from Mathematica Information Center (Site not responding. Last check: 2007-10-13)
		To develop geometric intuition, with an emphasis on how to use algebraic tools to resolve topological questions.
		This graduate course provides an introduction to Topology -- covering some of the basics of point-set topology, algebraic topology, and geometric topology.
		A freshman undergraduate student taking this course wrote a Java applet that implements the algorithm for classifying surfaces discussed in class.
	library.wolfram.com /infocenter/Courseware/277 (71 words)

	[No title]
		Recently, ideas and notions from mainstream "geometric" topology and algebraic topology have entered the scene in Concurrency Theory and Distributed Systems Theory (some of them based on older ideas).
		Among those are techniques borrowed from algebraic and geometric topology: Simplicial techniques have led to new theoretical bounds for coordination problems.
		This workshop aims at bringing together researchers from both the mathematical (geometry, topology, algebraic topology etc.) and computer scientific side (concurrency theorists, semanticians, researchers in distributed systems etc.) with an active interest in these or related developments.
	www.di.ens.fr /~goubault/getco.html (317 words)

	The Geometry Junkyard: Geometric Topology
		This area of mathematics is about the assignment of geometric structures to topological spaces, so that they "look like" geometric spaces.
		For instance, compact two dimensional surfaces can have a local geometry based on the sphere (the sphere itself, and the projective plane), based on the Euclidean plane (the torus and the Klein bottle), or based on the hyperbolic plane (all other surfaces).
		Riemann Surfaces and the Geometrization of 3-Manifolds, C.
	www.ics.uci.edu /~eppstein/junkyard/topo.html (559 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)

	18.937 - Topics in Geometric Topology - Spring 2006 (Site not responding. Last check: 2007-10-13)
		This course will focus on braid groups, mapping class groups, and their applications to the topology of plane curves and complex surfaces.
		The second half of the course will focus on applications to algebraic geometry (especially the study of plane curves and complex surfaces) and symplectic topology.
		We will in particular review Moishezon and Teicher's work on the braid monodromy of plane curves, as well as recent results on the topology of Lefschetz fibrations.
	www-math.mit.edu /~auroux/18.937 (497 words)

	Workshop Home Page
		Abstract: Artin groups, defined by presentations of a simple form, span a wide range of groups from braid groups, to free groups, to free abelian groups.
		They are closely related to Coxeter groups and mapping class groups and are associated with a variety of geometric objects.
		After a brief, general introduction to Artin groups, the lectures will focus on a class of Artin groups known as "right-angled" Artin groups.
	www.math.oregonstate.edu /~topology/workshop.htm (306 words)

	British Topology: resources
		Group Action Forum Focuses on the notion of group and the concept of symmetry in the mathematical sciences, prticularly, development, influence and application of the theory of transformation groups and related topics.
		Algebraic and Geometric Topology (AGT) (Electronic Journal: published at Warwick, Editors-in-Chief, Bob Oliver for Algebraic Topology and Marty Scharlemann for Geometric Topology)
		Daniel Murfet: The Rising Sea - impressive and growing collection of notes on aspects of algebraic geometry and relevant algebra.
	www.maths.gla.ac.uk /~ajb/btop/bt-resources.html (369 words)

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