Combinatorial Group Theory And Applications To Geometry PDF Download
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Author | : D.J. Collins |
Publisher | : Springer Science & Business Media |
Total Pages | : 248 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 3642580130 |
Download Algebra VII Book in PDF, ePub and Kindle
From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996
Author | : Clara Löh |
Publisher | : Springer |
Total Pages | : 390 |
Release | : 2017-12-19 |
Genre | : Mathematics |
ISBN | : 3319722549 |
Download Geometric Group Theory Book in PDF, ePub and Kindle
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
Author | : John Stillwell |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461243726 |
Download Classical Topology and Combinatorial Group Theory Book in PDF, ePub and Kindle
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.
Author | : Cynthia Hog-Angeloni |
Publisher | : Cambridge University Press |
Total Pages | : 428 |
Release | : 1993-12-09 |
Genre | : Mathematics |
ISBN | : 0521447003 |
Download Two-Dimensional Homotopy and Combinatorial Group Theory Book in PDF, ePub and Kindle
Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.
Author | : Roger C. Lyndon |
Publisher | : Springer |
Total Pages | : 354 |
Release | : 2015-03-12 |
Genre | : Mathematics |
ISBN | : 3642618960 |
Download Combinatorial Group Theory Book in PDF, ePub and Kindle
From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews
Author | : Gilbert Baumslag |
Publisher | : Springer Science & Business Media |
Total Pages | : 180 |
Release | : 1993-09-01 |
Genre | : Mathematics |
ISBN | : 9783764329211 |
Download Topics in Combinatorial Group Theory Book in PDF, ePub and Kindle
Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.
Author | : |
Publisher | : |
Total Pages | : 240 |
Release | : 1993 |
Genre | : Algebra |
ISBN | : |
Download Algebra Book in PDF, ePub and Kindle
Author | : Gilbert Baumslag |
Publisher | : Springer Science & Business Media |
Total Pages | : 235 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461397308 |
Download Algorithms and Classification in Combinatorial Group Theory Book in PDF, ePub and Kindle
The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.
Author | : Jack Koolen |
Publisher | : CRC Press |
Total Pages | : 188 |
Release | : 2008-07-02 |
Genre | : Mathematics |
ISBN | : 0203885767 |
Download Applications of Group Theory to Combinatorics Book in PDF, ePub and Kindle
Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state
Author | : Robert H. Gilman |
Publisher | : American Mathematical Soc. |
Total Pages | : 150 |
Release | : 1999 |
Genre | : Computers |
ISBN | : 0821810537 |
Download Groups, Languages and Geometry Book in PDF, ePub and Kindle
This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Geometric Group Theory and Computer Science held at Mount Holyoke College (South Hadley, MA). The conference was devoted to computational aspects of geometric group theory, a relatively young area of research which has grown out of an influx of ideas from topology and computer science into combinatorial group theory. The book reflects recent progress in this interesting new field. Included are articles about insights from computer experiments, applications of formal language theory, decision problems, and complexity problems. There is also a survey of open questions in combinatorial group theory. The volume will interest group theorists, topologists, and experts in automata and language theory.