This volume records the lectures given at a conference to celebrate Professor Ioan James' 60th birthday. Ioan James has made significant contributions to homotopy theory, highlighting problems and initiating new methods. The present volume contains papers from internationally distinguished researcher workers which lead on from recent and exciting breakthroughs. It will be important for all homotopy theorists as both a statement of current research and as a signpost for new directions.

### Contents

Preface; Publications of I. M. James; 1. Homotopy fixed points in the algebraic K-theory of certain infinite discrete groups G. Carlsson; 2. Applications of loop spaces to some problems in topology F. R. Cohen; 3. Invariants spheres and critical points M. C. Crabb; 4. Bitangent spheres and critical points Duan H.-E. Rees; 5. The enveloping ring of a II-algebra W. G. Dwyer and D. M. Kan; 6. Cohomologie des groupes symétriques et application de Quillen J. H. Gunawardena, J. Lannes and S. Zarati; 7. Looping Massey-Peterson towers J. R. Harper and H. R. Miller; 8. Characters and elliptic cohomology M. J. Hopkins; 9. Self maps of H-spaces J. R. Hubbuck; 10. Character rings in algebraic topology N. J. Kuhn; 11. The rank filtration of Quillen's Q-construction S. A. Mitchell; 12. Obstruction theory and the strict associativity of Morava K-theories C. A. Robinson; 13. Loop groups and harmonic maps G. B. Segal; 14. An almost groupoid structure for the space of (open) strings and implications for string field theory J. D. Stasheff; 15. Steenrod squares of polynomials R. M. W. Wood.