Two Dimensional Homotopy And Combinatorial Group Theory
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Two Dimensional Homotopy and Combinatorial Group Theory
Author | : Cynthia Hog-Angeloni,Wolfgang Metzler,Allan J. Sieradski |
Publsiher | : Unknown |
Total Pages | : 428 |
Release | : 1994 |
Genre | : Combinatorial group theory |
ISBN | : 1107366844 |
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This book considers the current state of knowledge in the geometric and algebraic aspects of two-dimensional homotopy theory.
Advances in Two Dimensional Homotopy and Combinatorial Group Theory
Author | : Wolfgang Metzler,Stephan Rosebrock |
Publsiher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 9781316600900 |
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Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.
Two Dimensional Homotopy and Combinatorial Group Theory
Author | : Cynthia Hog-Angeloni,Wolfgang Metzler,Allan J. Sieradski |
Publsiher | : Cambridge University Press |
Total Pages | : 428 |
Release | : 1993-12-09 |
Genre | : Mathematics |
ISBN | : 9780521447003 |
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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.
Combinatorial Group Theory and Topology
Author | : S. M. Gersten,John R. Stallings |
Publsiher | : Princeton University Press |
Total Pages | : 564 |
Release | : 1987-05-21 |
Genre | : Mathematics |
ISBN | : 9780691084107 |
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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.
Combinatorial and Geometric Group Theory
Author | : Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain |
Publsiher | : American Mathematical Soc. |
Total Pages | : 275 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780821828229 |
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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.
Invariants and Pictures
Author | : Vasiliĭ Olegovich Manturov,Igor Mikhailovich Nikonov,Denis Fedoseev,Seong-jeong Kim |
Publsiher | : Unknown |
Total Pages | : 357 |
Release | : 2020 |
Genre | : Combinatorial group theory |
ISBN | : 9811220123 |
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Computational and Geometric Aspects of Modern Algebra
Author | : Michael D. Atkinson,Michael Atkinson |
Publsiher | : Cambridge University Press |
Total Pages | : 290 |
Release | : 2000-06-15 |
Genre | : Mathematics |
ISBN | : 0521788897 |
Download Computational and Geometric Aspects of Modern Algebra Book in PDF, Epub and Kindle
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.
Recent Advances in Alexandrov Geometry
Author | : Gerardo Arizmendi Echegaray,Luis Hernández-Lamoneda,Rafael Herrera Guzmán |
Publsiher | : Springer Nature |
Total Pages | : 119 |
Release | : 2022-10-27 |
Genre | : Mathematics |
ISBN | : 9783030992989 |
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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.