Two-Dimensional Homotopy and Combinatorial Group Theory [Paperback]

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