# Combinatorial Methods in Topology and Algebraic Geometry

Share this page *Edited by *
*John R. Harper; Richard Mandelbaum*

This collection marks the recent resurgence of interest in
combinatorial methods, resulting from their deep and diverse
applications both in topology and algebraic geometry. Nearly thirty
mathematicians met at the University of Rochester in 1982 to survey
several of the areas where combinatorial methods are proving
especially fruitful: topology and combinatorial group theory, knot
theory, 3-manifolds, homotopy theory and infinite dimensional
topology, and four manifolds and algebraic surfaces. This material is
accessible to advanced graduate students with a general course in
algebraic topology along with some work in combinatorial group theory
and geometric topology, as well as to established mathematicians with
interests in these areas. For both student and professional
mathematicians, the book provides practical suggestions for research
directions still to be explored, as well as the aesthetic pleasures of
seeing the interplay between algebra and topology which is
characteristic of this field.

In several areas the book contains the first general exposition
published on the subject. In topology, for example, the
editors have included M. Cohen, W. Metzler and K. Sauerman's article
on “Collapses of \(K\times I\) and group presentations” and Metzler's “On the Andrews-Curtis-Conjecture and related problems.” In addition, J. M. Montesino has provided summary articles on both 3- and
4-manifolds.

# Table of Contents

## Combinatorial Methods in Topology and Algebraic Geometry

- Table of Contents ix10 free
- Introduction xi12 free
- Plenary lectures xiii14 free
- List of participants xv16 free
- Topology and Combinatorial Group Theory 120 free
- Collapses of K X I and Group Presentations 322
- On the Andrews-Curtis-Conjecture and related problems 3554
- Integral representations of Aut Fn and presentation classes of groups 5170
- A note on commutators and squares in free products 6988
- Rigidity of almost crystallographic groups 7392
- Finite graphs and free groups 7998
- A topological proof of a theorem of Brunner and Burns about M. Hall groups 85104

- Knot Theory 91110
- 3-Manifolds 139158
- Homotopy Theory And Infinite Dimensional Topology 199218
- Four Manifolds and Algebraic Surfaces 279298
- On fake [S3xS'#S2 x S2] 281300
- Manifolds having non-ample Norman bundles in quadrices 287306
- Lefschetz fibrations of Riemann surfaces and decompositions of complex elliptic surfaces 291310
- Algebraic surfaces and the arithmetic of braids, II 311330
- A note on moves and on irregular coverings of S4 345364