This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Fields Institute as part of the homotopy program during the year 1996. The papers in the volume describe current research in the subject, and all included works were refereed. Rather than being a summary of work to be published elsewhere, each paper is the unique source for the new material it contains. The book contains current research from international experts in the subject area, and presents open problems with directions for future research.
A functorial model for iterated Snaith splitting with applications to calculus of functors by G. Arone and M. Kankaanrinta Some remarks on the root invariant by R. R. Bruner On the Lusternik-Schnirelmann category of an iterated loop space by F. R. Cohen Thom spectra which are wedges of Eilenberg-MacLane spectra by F. R. Cohen and V. V. Vershinin Some properties of the relative Lusternik-Schnirelmann category by O. Comea The generating hypothesis revisited by E. S. Devinatz The periodic lambda algebra by B. Gray Rational $O(2)$-equivariant cohomology theories by J. P. C. Greenless The transcendence degree of the mod $p$ cohomology of finite Postnikov systems by J. Grodal Cogroups which are not suspensions. II by J. Harper Morava Hopf algebras and spaces $K(n)$ equivalent to finite Postnikov systems by M. J. Hopkins, D. C. Ravenel, and W. S. Wilson The transfer between rings of modular invariants of subgroups of $GL(n,p)$ by N. E. Kechagias Projectivity of Im $J$, cospherical classes and geometric dimension by K. Y. Lam and D. Randall Inert and lazy $n$-cones by J.-M. Lemaire Mod 3 truncated polynomial algebras over the Steenrod algebra by J. P. Lin A differential in the Adams spectral sequence for spheres by W.-H. Lin Some problems about phantom maps by C. A. McGibbon On some $BP *BP$-primitive elements related to the Kervaire invariant problemm by N. Minami Deterministic $p$-compact groups by J. M. Moller Space exponents for loop spaces of spheres by P. Selick On $f$-localization functors and connectivity by J.-Y. Tai On characterizations of rational homotopy types with some rational cyclic cohomologies by T. Yamaguchi.