Two-Dimensional Homotopy and Combinatorial Group Theory

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

Overview

The geometric and algebraic aspects of two-dimensional homotopy theory are both important areas of current research. Basic work on two-dimensional homotopy theory dates back to Reidemeister and Whitehead. The contributors to this book consider the current state of research beginning with introductory chapters on low-dimensional topology and covering crossmodules, Peiffer-Reid identities, and concretely discussing P2 theory. The chapters have been skillfully woven together to form a coherent picture, and the geometric nature of the subject is illustrated by over 100 diagrams. The final chapters round off neatly with a look at the present status of the conjectures of Zeeman, Whitehead and Andrews-Curtis.

Product Details

ISBN-13:	9780521447003
Publisher:	Cambridge University Press
Publication date:	12/09/1993
Series:	London Mathematical Society Lecture Note Series , #197
Pages:	428
Product dimensions:	5.94(w) x 8.94(h) x 0.83(d)

Table of Contents

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.