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Author: Cynthia Hog-Angeloni Publisher: Cambridge University Press ISBN: 0521447003 Category : Mathematics Languages : en Pages : 428
Book Description
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: S. M. Gersten Publisher: Princeton University Press ISBN: 0691084106 Category : Mathematics Languages : en Pages : 564
Book Description
Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge, Utah. Contributors to the book include Roger Alperin, Hyman Bass, Max Benson, Joan S. Birman, Andrew J. Casson, Marshall Cohen, Donald J. Collins, Robert Craggs, Michael Dyer, Beno Eckmann, Stephen M. Gersten, Jane Gilman, Robert H. Gilman, Narain D. Gupta, John Hempel, James Howie, Roger Lyndon, Martin Lustig, Lee P. Neuwirth, Andrew J. Nicas, N. Patterson, John G. Ratcliffe, Frank Rimlinger, Caroline Series, John R. Stallings, C. W. Stark, and A. Royce Wolf.
Author: Sean Cleary Publisher: American Mathematical Soc. ISBN: 0821828223 Category : Mathematics Languages : en Pages : 275
Book Description
This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compact Riemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.
Author: Michael D. Atkinson Publisher: Cambridge University Press ISBN: 9780521788892 Category : Mathematics Languages : en Pages : 290
Book Description
This book comprises a collection of papers from participants at the IMCS Workshop on Computational and Geometric Aspects of Modern Algebra, held at Heriot-Watt University in 1998. Written by leading researchers, the papers cover a wide range of topics in the vibrant areas of word problems in algebra and geometric group theory. This book represents a timely record of recent work and provides an indication of the key areas of future development.
Author: Gerardo Arizmendi Echegaray Publisher: Springer Nature ISBN: 3030992985 Category : Mathematics Languages : en Pages : 119
Book Description
This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field. It contains enhanced versions of the lecture notes of the two mini-courses plus those of one research talk given at CIMAT. Peter Petersen’s part aims at presenting various rigidity results about Alexandrov spaces in a way that facilitates the understanding by a larger audience of geometers of some of the current research in the subject. They contain a brief overview of the fundamental aspects of the theory of Alexandrov spaces with lower curvature bounds, as well as the aforementioned rigidity results with complete proofs. The text from Fernando Galaz-García’s minicourse was completed in collaboration with Jesús Nuñez-Zimbrón. It presents an up-to-date and panoramic view of the topology and geometry of 3-dimensional Alexandrov spaces, including the classification of positively and non-negatively curved spaces and the geometrization theorem. They also present Lie group actions and their topological and equivariant classifications as well as a brief account of results on collapsing Alexandrov spaces. Jesús Nuñez-Zimbrón’s contribution surveys two recent developments in the understanding of the topological and geometric rigidity of singular spaces with curvature bounded below.
Author: D.J. Collins Publisher: Springer Science & Business Media ISBN: 9783540637042 Category : Mathematics Languages : en Pages : 252
Book Description
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: C. M. Campbell Publisher: Cambridge University Press ISBN: 1316467910 Category : Mathematics Languages : en Pages : 503
Book Description
Every four years, leading researchers gather to survey the latest developments in all aspects of group theory. Since 1981, the proceedings of those meetings have provided a regular snapshot of the state of the art in group theory and helped to shape the direction of research in the field. This volume contains selected papers from the 2013 meeting held in St Andrews. It begins with major articles from each of the four main speakers: Emmanuel Breuillard (Paris-Sud), Martin Liebeck (Imperial College London), Alan Reid (Texas) and Karen Vogtmann (Cornell). These are followed by, in alphabetical order, survey articles contributed by other conference participants, which cover a wide spectrum of modern group theory.
Author: Wolfgang Metzler
Author: Wolfgang Metzler
Author: Cynthia Hog-Angeloni
Author: Cynthia Hog-Angeloni
Author: S. M. Gersten
Author: Sean Cleary
Author: Vasiliĭ Olegovich Manturov
Author: Michael D. Atkinson
Author: Gerardo Arizmendi Echegaray
Author: D.J. Collins
Author: C. M. Campbell