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The Geometry of the Word Problem for Finitely Generated Groups (Advanced Courses in Mathematics) [Paperback]

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Item description for The Geometry of the Word Problem for Finitely Generated Groups (Advanced Courses in Mathematics) by Noel Brady, Tim Riley & Hamish Short...

The origins of the word problem are in group theory, decidability and complexity, but, through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-scale geometry, including topics such as soap films, isoperimetry, coarse invariants and curvature. The first part introduces van Kampen diagrams in Cayley graphs of finitely generated, infinite groups; it discusses the van Kampen lemma, the isoperimetric functions or Dehn functions, the theory of small cancellation groups and an introduction to hyperbolic groups.One of the main tools in geometric group theory is the study of spaces, in particular geodesic spaces and manifolds, such that the groups act upon. The second part is thus dedicated to Dehn functions, negatively curved groups, in particular, CAT(0) groups, cubings and cubical complexes.In the last part, filling functions are presented from geometric, algebraic and algorithmic points of view; it is discussed how filling functions interact, and applications to nilpotent groups, hyperbolic groups and asymptotic cones are given. Many examples and open problems are included.

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Item Specifications...


Pages   206
Est. Packaging Dimensions:   Length: 0.75" Width: 6.75" Height: 9.25"
Weight:   1.3 lbs.
Binding  Softcover
Release Date   Jan 22, 2007
Publisher   Birkhäuser Basel
ISBN  3764379499  
ISBN13  9783764379490  


Availability  0 units.


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Product Categories

1Books > Special Features > New & Used Textbooks > Sciences > Mathematics > Algebra & Trigonometry
2Books > Special Features > New & Used Textbooks > Sciences > Mathematics > Geometry
3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Geometry & Topology > General Geometry
4Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Algebra > General
5Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Combinatorics
6Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Group Theory
7Books > Subjects > Science > General
8Books > Subjects > Science > Mathematics > General
9Books > Subjects > Science > Mathematics > Geometry & Topology > General Geometry
10Books > Subjects > Science > Mathematics > Pure Mathematics > Algebra > General
11Books > Subjects > Science > Mathematics > Pure Mathematics > Combinatorics
12Books > Subjects > Science > Mathematics > Pure Mathematics > Group Theory



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