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	Geometric group theory - Wikipedia, the free encyclopedia
		Geometric group theory and combinatorial group theory are two closely related branches of mathematics, which study infinite discrete groups.
		Geometric group theory uses topological and geometric methods to study groups; the main philosophy is to deduce information about a group by analyzing how it acts on topological spaces.
		hyperbolicity of a group, and the boundary of a hyperbolic group
	en.wikipedia.org /wiki/Geometric_group_theory (348 words)

	20: Group Theory and Generalizations
		Group theory can be considered the study of symmetry: the collection of symmetries of some object preserving some of its structure forms a group; in some sense all groups arise this way.
		Groups acting on topological spaces are the basis of equivariant topology and homotopy theory in Algebraic Topology.
		Nielsen's theorem: subgroups of free groups are free.
	www.math.niu.edu /~rusin/known-math/index/20-XX.html (2774 words)

	Amazon.ca: Topics in Geometric Group Theory: Books: Pierre de la Harpe,Pierre De La Harpe (Site not responding. Last check: 2007-11-05)
		Groups as abstract structures were first recognized by mathematicians in the nineteenth century.
		Groups are, of course, sets given with appropriate "multiplications," and they are often given together with actions on interesting geometric objects.
		More precisely, a finitely-generated group can be seen as a metric space, the distance between two points being defined "up to quasi-isometry" by some "word length," and this gives rise to a very fruitful approach to group theory.
	www.amazon.ca /Topics-Geometric-Theory-Pierre-Harpe/dp/0226317196 (540 words)

	What is Geometric Group Theory? (Site not responding. Last check: 2007-11-05)
		A simple definition of Geometric group theory is that it is the study of groups as geometric objects.
		Geometric group theory draws upon techniques from, and solves problems in the theory of 3-manifolds, hyperbolic geometry, combinatorial group theory, Lie groups...
		When the group G is infinite, its Cayley graph reflects large-scale geometric features which can have a profound effect on the algebra of G.
	www.math.mcgill.ca /wise/ggt/cayley.html (307 words)

	The Math Forum - Math Library - Group Theory (Site not responding. Last check: 2007-11-05)
		Group Theory is a branch of algebra, but has strong connections with almost all parts of mathematics.
		Group theory takes an abstract approach, dealing with many mathematical systems at once and requiring only that a mathematical system obey a few simple rules, seeking then to find properties common to all systems that obey these few rules.
		A short article designed to provide an introduction to finite groups - their internal properties: all those results about group theory for which a consideration of the order of elements is a central part of the question.
	mathforum.org /library/topics/group_theory (2240 words)

	Karoline Pershell
		Geometric group theory is the study of groups as geometric objects.
		There are two ways to approach this: we can either study the geometry of a group based on how it acts on geometric spaces, or we can study the group as a geometric space in its own right, via the Cayley graph.
		A short course in geometric group theory These notes by Walter Neumann and Michael Shapiro were prepared for the ANU Workshop in 1996.
	math.rice.edu /~pershell/projects.htm (433 words)

	Mathematical Sciences Research Institute - Geometric Group Theory (Site not responding. Last check: 2007-11-05)
		Geometric group theory is relatively young field but with older and deeper roots in which groups were studied from combinatorial and topological perspectives.
		Topological methods in group theory focused on the cohomology of groups and their finiteness properties, and hence viewed groups as essentially topological ob jects.
		We will bring people from the various branches of geometric group theory together to work on some of the many longer-standing open questions in the field that are now being studied from fresh and promising perspectives, and to further strengthen the connections the field has to the other branches of mathematics.
	www.msri.org /calendar/programs/ProgramInfo/245/show_program (312 words)

	Geometric Group Theory - Cambridge University Press (Site not responding. Last check: 2007-11-05)
		For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.
		The geometric invariants of a group - a survey with emphasis on the homological approach; 4.
		A group theoretic proof of the torus theorem; 13.
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521435293 (191 words)

	Group Theory - Research - Newcastle University (Site not responding. Last check: 2007-11-05)
		A major aim of combinatorial group theory is the extraction of information from presentations of groups by generators and relations.
		These arise from groups of matrices which fix quadratic or other forms, and so are intimately connected with the geometry of vector and projective spaces.
		A second major aim is to discover new geometrical figures, often over finite fields, with a rich and picturesque structure with interesting symmetry groups.
	www.ncl.ac.uk /math/research/pure/group_theory.htm (583 words)

	ARCC Workshop: Boundaries in Geometric Group Theory (Site not responding. Last check: 2007-11-05)
		A variety of different constructions of boundaries at infinity have long played an important role in geometric group theory and related areas such as Kleinian groups, rigidity theory for lattices, 3-manifolds, and nonpositive curvature.
		Papers by Rips-Sela, Bowditch, Papasoglu, Dunwoody-Swenson, and Dunwoody-Sageev established JSJ decompositions for finitely presentable groups; these results either use boundary dynamics in their proofs, or use boundary structure to establish quasi-isometry invariance of the splittings.
		Bowditch and Swenson have shown that a group is necessarily hyperbolic provided it has an action on a compact space satisfying suitable dynamical properties.
	www.aimath.org /ARCC/workshops/groupboundaries.html (403 words)

	Fields Institute - Geometric Methods in Group Theory
		The goal of this workshop is to bring top specialists in this area to Carleton to give introductory courses that should be accessible to graduate students and of use to researchers in group theory, low-dimensional topology, analysis, algebraic geometry and related areas.
		Surprisingly many of the groups traditionally studied by combinatorial group theorists are turning out to act properly on CAT(0) cube complexes.
		This is leading to an increased and more unified understanding of these groups, as well as the resolution of some of the algebraic problems that were first raised in combinatorial group theory but were unapproachable without geometric methods.
	www.fields.utoronto.ca /programs/scientific/06-07/group_theory (538 words)

	Graduate School : Pure Mathematics (Site not responding. Last check: 2007-11-05)
		Actions of groups on metric spaces have played an important role in developing our understanding of geometry and group theory.
		The group action allows us to obtain information about the space, while the global geometry of the space often gives important information about the structure of the given group.
		Members of the research group have collaborated with mathematicians from California, Barcelona and Regensburg as well as institutions throughout the UK.
	www.maths.soton.ac.uk /graduate/pure/geometric.shtml (229 words)

	Geometric group theory books, find the lowest prices
		Combinatorial and Geometric Group Theory : Edinburgh 1993
		Geometric Group Theory : Proceedings of the Symposium Held in Sussex 1991 Asymptotic Invariants of Infinite Groups, M. Gromov
		Geometric Group Theory : Proceedings of a Special Research Quarter at the Ohio State University, Spring 1992
	www.allbookstores.com /Geometric_Group_Theory_st.html (345 words)

	[No title]
		An international team that includes Vanderbilt Mathematics Professors Alexander Olshanskii and Mark Sapir has been awarded a major grant by the National Science Foundation to tackle several unsolved problems in the areas of algebra and geometric group theory.
		The “Asymptotic and Probabilistic Methods in Geometric Group Theory” project brings together proven leaders in geometric group theory and related fields of mathematics – including two Fields Medalists – in a Focused Research Group.
		The problems they will study are of central importance in algebra and geometric group theory, and solutions to them will have an effect on many other areas of mathematics.
	sitemason.vanderbilt.edu /page/ei5jqg (354 words)

	595-05
		Lecture notes on Geometric Group Theory [pdf file], by Michael Kapovich (be aware that there are lots of misprints in this file);
		Geometric Group theory in the last 30 years.
		At the end of the course I will expect each student to make a presentation on some paper (I will provide a number of choices) that is reasonably short, self-contained and yet concerns some recent developments in Geometric Group Theory.
	www.math.uiuc.edu /~kapovich/595-05/595-05.html (296 words)

	New York Group Theory Cooperative (Site not responding. Last check: 2007-11-05)
		MINI-CONFERENCE: Group Theory and Topology at CCNY, Oct 22, 2004
		Archives of preprints in combinatorial and geometric group theory
		Lecture notes on group theory and related topics
	zebra.sci.ccny.cuny.edu /web/nygtc/nygtc-main.html (93 words)

	Group Theory in Perception, Robotics, and Design (Site not responding. Last check: 2007-11-05)
		The last decade has seen an enormous expansion in the use of group theory in the perceptual, robotic and design disciplines.
		These disciplines are inherently geometric, and group theory is the language of geometry.
		This course will examine the use of group theory in human perception, computer vision, robot manipulation, object-oriented software, 3D solid modeling, mechanical CAD/CAM, assembly planning, and architectural CAD.
	www.rci.rutgers.edu /~mleyton/Group_Theory_Course.htm (124 words)

	Atlas: Combinatorial and Geometric Group Theory - List of Speakers
		Stefan Forcey Categorified Associahedra and alternate blueprints for a free group element.
		Alexei Miasnikov On elementary theories of free groups
		Alex Lubotzky Linear representations of the automorphism group of a free group
	atlas-conferences.com /cgi-bin/abstract/caqu-01 (757 words)

	Montreal Geometric Group Theory Seminar
		Theorem: Let G be an arithmetic hyperbolic group of simple type.
		To a graph G is associated a partially commutative group P
		example of such a group whose presentation is known.
	www.math.mcgill.ca /wise/ggt/seminar.html (450 words)

	Geometric Topology at UW-Milwaukee (Site not responding. Last check: 2007-11-05)
		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)

	Conferences
		Jan 2007 New Orleans - Geometric groups on the gulf
		Sept 2006 Malaga, Spain - Groups in Geometry and Topology
		Mar 2006 Mobile, Alabama - Geometric Groups on the Gulf
	www.math.ucsb.edu /~mccammon/geogrouptheory/conferences.html (334 words)

	UM Department of Mathematics: University of Michigan Department of Mathematics: Topology
		Geometric methods in group theory, representation theory of discrete groups,
		The topology seminar is held weekly during the Fall and Winter terms.
		This is an informal forum which welcomes talks on any topic of geometric interest.
	www.math.lsa.umich.edu /research/topology (332 words)

	Geometric Group Theory: Volume 2 reviews and ratings at MSN Shopping
		Geometric Group Theory: Volume 2 reviews and ratings at MSN Shopping
		Geometric Group Theory: Volume 2: Reviews and ratings
		Drag your mouse across the stars to select a rating from 1 to 5 stars, and then click to save it.
	shopping.msn.com /Reviews.aspx?itemId=2905902 (76 words)

	AMS Special Session on Geometric Group Theory
		9:00 Matt Brin: Birth, death and the braid group.
		2:30 Mark Feighn: Free decompositions of graphs of free groups.
		9:30 Andrew Casson:Trivializations of group presentations and the Andrews-Curtis conjecture.
	www.sci.ccny.cuny.edu /~cleary/boston.html (428 words)

	ARCC Workshop: Problems in Geometric Group Theory (Site not responding. Last check: 2007-11-05)
		This workshop, sponsored by AIM and the NSF, will be devoted to compiling a list of unsolved and partially solved problems in geometric group theory.
		The list will be organized into various subfields of geometric group theory and other fields that have substantial overlap with geometric group theory.
		The problems will be annotated with special cases, relationships among the problems, broader implications, and progress to date.
	www.aimath.org /ARCC/workshops/geomgpthy.html (317 words)

	Geometric Group Theory
		The Geometric Group Theory Page provides information and resources about geometric group theory and low-dimensional topology, although the links sometimes stray into neighboring fields.
		This page is meant to help students, scholars, and interested laypersons orient themselves to this large and ever-expanding body of work.
		Organizations: Institutions where geometric group theory is studied, as well as general mathematical organizations
	www.math.ucsb.edu /~jon.mccammond/geogrouptheory/index.html (116 words)

	Jason Behrstock's Home Page
		My primary interests are in geometric group theory and low dimensional topology.
		• A revised version of my thesis, also entitled "Asymptotic Geometry of the Mapping Class Group and Teichmuller Space" (May 2005); this version has strengthened versions of several of the results from my Thesis plus a proof that mapping class groups and Teichmuller space each have tree-graded asymptotic cones.
		• "Quasi-isometric classification of graph manifolds groups" with W.
	www.math.columbia.edu /~jason (364 words)

	AMS Special Session on Geometric Group Theory
		9:30 A finitely-presented solvable group with a small quasi-isometry group.
		4:30 On the local and global structure of the automorphism graph of a free group.
		8:30 Solvability in Groups of Piecewise-linear Homeomorphisms of the Unit Interval.
	www.sci.ccny.cuny.edu /~cleary/bard.html (914 words)

	John R. Stallings's Home Page (Site not responding. Last check: 2007-11-05)
		Notes: (1) is related to H Kneser's paper of 1929, and includes matters related to commutators in free products, the splitting of 3-manifolds according to splitting of the fundamental group, Grushko-Neumann-Wagner theorems on generators of free products, etc.
		(2) is related to a paper by JHC Whitehead in 1936, and has to do with cut vertices in graphs and decompositions of free groups into free products.
		Paper written in 1974, TeXed in 2002, on "An Extension Theorem for Euler characteristics of groups".
	www.math.berkeley.edu /~stall (267 words)

	Geometric Group Theory Down Under (Site not responding. Last check: 2007-11-05)
		These are the proceedings of the Special Year in Geometric Group Theory held at the Australian National University and Melbourne University in 1996.
		The papers give an overall picture of the latest research in the field.
		Topics include: theory of algebraic groups; theory of automatic and hyperbolic groups; convergence groups; distortion of subgroups; Artin groups and braid groups; amenable groups; combinatorial approaches to conformal structure; algebraic and geometric automorphism groups, and geometric invariants of groups.
	www.booknews.co.uk /Books/1368.htm (85 words)

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