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  3. Two-Dimensional Homotopy and Combinatorial Group Theory
  • Cited by 22
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
1993
Online ISBN:
9780511629358
DOI:
https://doi.org/10.1017/CBO9780511629358
Subjects:
Mathematics (general), Mathematics, Geometry and Topology, Algebra
Series:
London Mathematical Society Lecture Note Series (197)
Information

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.

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