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Computational and Geometric Aspects of Modern Algebra
A collection of papers from leading researchers in algebra and geometric group theory.
Advances in Two-Dimensional Homotopy and Combinatorial Group Theory
Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.
Encyclopaedia of Mathematics
This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Knots, Low-Dimensional Topology and Applications
This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymer...
Two-Dimensional Homotopy and Combinatorial Group Theory
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.
Geometric and Cohomological Methods in Group Theory
An extended tour through a selection of the most important trends in modern geometric group theory.
Max Dehn
Max Dehn (1878?1952) is known to mathematicians today for his seminal contributions to geometry and topology?Dehn surgery, Dehn twists, the Dehn invariant, etc. He is also remembered as the first mathematician to solve one of Hilbert?s famous problems. However, Dehn's influence as a scholar and teacher extended far beyond his mathematics. Dehn also lived a remarkable life, described in this book in three phases. The first phase focuses on his early career as one of David Hilbert?s most gifted students. The second, after World War I, treats his time in Frankfurt where he led an intimate community of mathematicians in explorations of historical texts. The final phase, after 1938, concerns his flight from Nazi Germany to Scandinavia and eventually to the United States where, after various teaching experiences, the Dehns settled at iconic Black Mountain College. This book is a collection of essays written by mathematicians and historians of art and science. It treats Dehn?s mathematics and its influence, his journeys, and his remarkable engagement in history and the arts. A great deal of the information found in this book has never before been published.
History of Topology
Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Lower Central and Dimension Series of Groups
A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series, which consists of the subgroups determined by the augmentation powers, is a challenging task. This monograph presents an exposition of different methods for investigating this relationship. In addition to group theorists, the results are also of interest to topologists and number theorists. The approach is mainly combinatorial and homological. A novel feature is an exposition of simplicial methods for the study of problems in group theory.
Mathematical Reviews
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