Contemporary Mathematics 1985; 349 pp; softcover Volume: 44 Reprint/Revision History: reprinted 1988 ISBN10: 0821850393 ISBN13: 9780821850398 List Price: US$53 Member Price: US$42.40 Order Code: CONM/44
 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, 3manifolds, 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 AndrewsCurtisConjecture and related problems." In addition, J. M. Montesino has provided summary articles on both 3 and 4manifolds. Table of Contents Topology and Combinatorial Group Theory  M. Cohen, W. Metzler, and K. Sauermann  Collapses of \(K\times I\) and group presentations
 W. Metzler  On the AndrewsCurtisConjecture and related problems
 M. Lustig and W. Metzler  Integral representations of \(AutF^n\) and presentation classes of groups
 R. Goldstein and E. C. Turner  A note on commutators and squares in free products
 K. B. Lee and F. Raymond  Rigidity of almost crystallographic groups
 J. R. Stallings  Finite graphs and free groups
 C. Tretkoff and M. Tretkoff  A topological proof of a theorem of Brunner and Burns about M. Hall groups
Knot Theory  D. Gabai  The Murasugi sum is a natural geometric operation II
 L. H. Kauffman  The Arf Invariant of classical knots
 W. B. R. Lickorish  The unknotting number of a classical knot
 B. Trace  A general position theorem for surfaces in Euclidean \(4\)space
3Manifolds  A. L. Edmonds  n the equivariant Dehn lemma
 J. Hempel  Virtually Haken manifolds
 J. M. Montesinos  Lectures on \(3\)fold simple coverings and \(3\)manifolds
 H. S. Oh  The Witt classes of Seifert manifolds
 M. Scharlemann  Outermost forks and a theorem of Jaco
 J. R. Stallings  Surfaces in \(3\)manifolds
Homotopy Theory and Infinite Dimensional Topology  M. G. Barratt  Taming Hopf invariants
 F. R. Cohen  Artin's braid groups and classical homotopy theory
 L. R. Rubin  More compacta of infinite cohomological dimension
 A. Zabrodsky  Endomorphisms in the homotopy category
Four Manifolds and Algebraic Surfaces  S. Akbulut  On fake \(S^3\sim \times S^1 \# S^2\times S^2\)
 N. Goldstein  Manifolds having nonample Norman bundles in quadrices
 R. Mandelbaum  Lefschetz fibrations of Riemann surfaces and decompositions of complex elliptic surfaces
 B. Moishezon  Algebraic surfaces and the arithmetic of braids, II
 J. Montesinos  A note on moves and on irregular coverings of \(S^4\)
