Advances in Two-Dimensional Homotopy and Combinatorial Group Theory

This volume presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Building on the foundations laid a quarter of a century ago in the volume Two-dimensional Homotopy and Combinatorial Group Theory (LMS 197), the editors here bring together much remarkable progress that has been obtained in the intervening years. And while the fundamental open questions, such as the Andrews–Curtis Conjecture and the Whitehead asphericity problem remain to be (fully) solved, this book will provide both students and experts with an overview of the state of the art and work in progress. Ample references are included to the LMS 197 volume, as well as a comprehensive bibliography bringing matters entirely up to date.

Preface Wolfgang Metzler and Stephan Rosebrock; List of contributors; 1. A survey of recent progress on some problems in 2-dimensional topology Jens Harlander; Appendix: geometric realization for algebraic 2-complexes with finite fundamental group F. Rudolf Beyl and Jens Harlander; 2. Further results concerning the Andrews–Curtis conjecture and its generalizations Cynthia Hog-Angeloni and Wolfgang Metzler; 3. Aspects of TQFT and computational algebra Holger Kaden and Simon King; 4. Labelled oriented trees and the Whitehead conjecture Stephan Rosebrock and Jens Harlander; 5. 2-complexes and 3-manifolds Janina Glock, Cynthia Hog-Angeloni and Sergei Matveev; 6. The relation gap problem Jens Harlander; 7. On the relation gap problem for free products Cynthia Hog-Angeloni and Wolfgang Metzler; References; Index; Erratum.

Wolfgang Metzler works in the Institute of Mathematics at Johann Wolfgang Goethe-Universität Frankfurt, Germany.
Stephan Rosebrock works in the Institute of Mathematics and Computer Science at Pädagogische Hochschule Karlsruhe, Germany.