Topology: past, present and future -- The work of Edgar H. Brown, Jr. in Topology -- Homology representations of finite transformation groups -- Homotopy exponents for spaces of category two -- On the complex bordism of classifying spaces -- On equivariant maps and immersions of real projective spaces -- Cogroups which are not suspensions -- Instantons and homotopy -- On real homotopy theory -- Some remarks on the space Im J -- A new spectrum related to 7-connected cobordism -- Aspherical manifolds without smooth or PL structure -- Homology with simplicial coefficients -- On the double suspension -- A whitehead product for track groups -- Minimal atlases of real projective spaces -- Higher homotopy associativity -- Homotopy approximations for classifying spaces of compact lie groups -- Cyclic homology and characteristic classes of bundles with additional structures -- Morava K-theories and infinite loop spaces -- Lie groups from a homotopy point of view -- Order of the identity map of the Brown-Gitler spectrum -- Topology of the intersection of quadrics in ?2 -- Orientations for Poincaré duality spaces and applications -- A double coset formula for levi subgroups and splitting BGL n -- Browder-Fröhlich symbols -- K-theory homology of spaces -- Stirling and Bernoulli numbers for complex oriented homology theory -- Composition products in RHom, and ring spectra of derived endomorphisms -- Convexity and root closure in negatively curved manifolds -- Cohomology of finite groups and brown-peterson cohomology -- The artin-hasse logarithm for ?-rings -- Higher cohomology operations that detect homotopy classes -- Problem session for homotopy theory -- H-spaces -- K and L-theory -- Manifolds & bordism -- Transformation groups.

These are proceedings of an International Conference on Algebraic Topology, held 28 July through 1 August, 1986, at Arcata, California. The conference served in part to mark the 25th anniversary of the journal Topology and 60th birthday of Edgar H. Brown. It preceded ICM 86 in Berkeley, and was conceived as a successor to the Aarhus conferences of 1978 and 1982. Some thirty papers are included in this volume, mostly at a research level. Subjects include cyclic homology, H-spaces, transformation groups, real and rational homotopy theory, acyclic manifolds, the homotopy theory of classifying spaces, instantons and loop spaces, and complex bordism.