Two-Dimensional Homotopy and Combinatorial Group Theory

This book considers the current state of knowledge in the geometric and algebraic aspects of two-dimensional homotopy theory.

Cynthia Hog-Angeloni (Edited by), Wolfgang Metzler (Edited by), Allan J. Sieradski (Edited by)

9780521447003, Cambridge University Press

Paperback, published 9 December 1993

428 pages, 115 b/w illus.
22.7 x 15.1 x 2.1 cm, 0.592 kg

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.

1. Geometric aspects of two-dimensional complexes C. Hog-Angeloni and W. Metzler
2. Algebraic topology for two-dimensional complexes A. J. Sieradski
3. Homotopy and homology classification of 2-complexes M. P. Latiolais
4. Crossed modules and P2 homotopy modules M. Dyer
5. Calculating generators of P2 W. Bogley and S. J. pride
6. Applications of diagrams to decision processes G. Huck and S. Rosebrock
7. Fox ideals, N-torsion and applications to groups and 3-manifolds M. Lustig
8. (Singular) 3-manifolds C. Hog-Angeloni and A. Sieradski
9. Cancellation results for 2-complexes and 4-manifolds and some applications I. Hambleton and M. Kreck
10. J. H. C. Whitehead's asphericity question W. Bogley
11. Zeeman's collapsing conjecture S. Matveev and D. Rolfsen
12. The Andrews-Curtis conjecture and its generalizations C. Hog-Angeloni and W. Metzler.

Subject Areas: Groups & group theory [PBG]