Two-Dimensional Homotopy and Combinatorial Group Theory PDF Download
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Author: Cynthia Hog-Angeloni
Publisher: Cambridge University Press
ISBN: 0521447003
Category : Mathematics
Languages : en
Pages : 428
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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: Cynthia Hog-Angeloni
Publisher: Cambridge University Press
ISBN: 0521447003
Category : Mathematics
Languages : en
Pages : 428
Get Book Here
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: Wolfgang Metzler
Publisher: Cambridge University Press
ISBN: 1316600904
Category : Mathematics
Languages : en
Pages : 193
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Book Description
Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.
Author: Cynthia Hog-Angeloni
Publisher:
ISBN: 9781107361935
Category : MATHEMATICS
Languages : en
Pages : 426
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Book Description
This book considers the current state of knowledge in the geometric and algebraic aspects of two-dimensional homotopy theory.
Author: F. E. A. Johnson
Publisher: Cambridge University Press
ISBN: 9780521537490
Category : Mathematics
Languages : en
Pages : 282
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Book Description
This 2003 book deals with two fundamental problems in low-dimensional topology with an eye on wider context.
Author: R. A. Bailey
Publisher: Cambridge University Press
ISBN: 1009465945
Category : Mathematics
Languages : en
Pages : 452
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Book Description
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
Author: S. Müller-Stach
Publisher: Cambridge University Press
ISBN: 9780521545471
Category : Mathematics
Languages : en
Pages : 314
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Book Description
Lecture notes for graduates or researchers wishing to enter this modern field of research.
Author: F. Blanchard
Publisher: Cambridge University Press
ISBN: 9780521796606
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This book is devoted to recent developments in symbolic dynamics, and it comprises eight chapters. The first two are concerned with the study of symbolic sequences of 'low complexity', the following two introduce 'high complexity' systems. The later chapters go on to deal with more specialised topics including ergodic theory, number theory, and one-dimensional dynamics.
Author: Mark Pollicott
Publisher: Cambridge University Press
ISBN: 0521576881
Category : Mathematics
Languages : en
Pages : 496
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Book Description
A mixture of surveys and original articles that span the theory of Zd actions.
Author: André Joyal
Publisher: Cambridge University Press
ISBN: 9780521558303
Category : Mathematics
Languages : en
Pages : 136
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Book Description
This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.
Author: Thomas Peterfalvi
Publisher: Cambridge University Press
ISBN: 9780521646604
Category : Mathematics
Languages : en
Pages : 166
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Book Description
The famous and important theorem of W. Feit and J. G. Thompson states that every group of odd order is solvable, and the proof of this has roughly two parts. The first part appeared in Bender and Glauberman's Local Analysis for the Odd Order Theorem which was number 188 in this series. This book provides the character-theoretic second part and thus completes the proof. All researchers in group theory should have a copy of this book in their library.
