By I. M. James (auth.), Gunnar Carlsson, Ralph Cohen, Haynes Miller, Douglas Ravenel (eds.)

These are lawsuits of a world convention on Algebraic Topology, held 28 July via 1 August, 1986, at Arcata, California. The convention served partly to mark the twenty fifth anniversary of the magazine Topology and sixtieth birthday of Edgar H. Brown. It preceded ICM 86 in Berkeley, and used to be conceived as a successor to the Aarhus meetings of 1978 and 1982. a few thirty papers are incorporated during this quantity, more often than not at a study point. topics contain cyclic homology, H-spaces, transformation teams, actual and rational homotopy concept, acyclic manifolds, the homotopy idea of classifying areas, instantons and loop areas, and intricate bordism.

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S. "On t h e Origin Spheres", of Infinite Topology in t h e Minimal Yol. 230(1977), Homotopy Groups of Families Vol. Models pp. the 8(1989), of 173-199. Union of in pp. 52 Spheres", 18. M. J. James, 62(1955), 19. -M. London pp. Soc. 30(1955), Spaces, pp. Annals of 154-172. Math. 170-197. Lemaire, Lacets, Math. "Reduced Alg~bres Lecture Notes Connexes in Math. de........ Springer-Verlag, 1974. 20. -M. Lemaire, de P o i n c a r 6 "Anneaux irrationnelles", Springer-Verlag, 21. A. McGibbon Complexes No.

V k ) generalizes the antipodal map on spheres. f: S ~ --* Vk(R'*) equivariant with respect to cr and the set of sections in the bundle of k-frames associated to m ~ where ~, denotes the Hopf line bundle over n-dimensional real projective space P " . In particular, P~ immerses differentiably in R "+k for k > 0 if and only if there exists a map f : S" --~ Tin+~(R "+k+ 1) equivariant with respect to a. ~) of tr~ (V~(R"~)) to the existence of an equivariant map g: S n+l --* V~(R"*) which coincides with f on S " - 1 .

75 (1969), 1293-1298. W. J. A. Wolf, "Spaces of constant curvature," McGraw-Hill, 1967. Rider College, Lawrenceville, NJ 08648 Lehigh University, Bethlehem, Pa. 18015 ON EQUIVARIANT MAPS AND IMMERSIONS OF REAL PROJECTIVE SPACES by A. J . B e r r i c k and D u a n e R a n d a l l National University of Singapore Pontificia Universidade Catolica Kent Ridge 0511, Singapore Rio de Janeiro, Brazil Let V~(R'*) denote the Stiefel manifold of orthonormal k-frames in Euclidean m-space. The antipodal involution a on Vk (R "~) given by a ( v l , .

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