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Lecture Notes in Mathematics Lecture Notes in Mathematics For information about Vols. 1-1145 please contact your bookseller Vol. 1173: H. DeHs, M. Knebusch, Locally Semialgebraic Spaces. XVI, or Springer-Verlag. 329 pages. 1g95, Vol. 1146: 5eminaire d'Aigebre Paul Dubreil et Marie-Paula Malliavin. Vol. 1174: Categories in Continuum Physics, Buffalo 1982. Seminar. Proceedings, 1g63-1984. Edite par M.-P. Malliavin. IV, 420 pages. Edited by F.W. Lawvere and S.H. Schanuel. V, t26 pages. t986. 1985. Vol. 1175: K. Mathiak, Valuations of Skew Fields and Projective Vol. 1147: M. Wschebor, Surfaces Aleatoires. VII, 11t pages. 1985. Hjelmslev Spaces. VII, 116 pages. 1986. Vol. 1t48: Mark A. Kon, Probability Distributions in Quantum Statistical Vol. 1176: R.R. Bruner, J.P. May, J.E. McClure, M. Steinberger, Mechanics. V, 12t pages. 1985. Hoo Ring Spectra and their Applications. VII, 388 pages. 1988. Vol. 1149: Universal Algebra and Lattice Theory. Proceedings, 1984. Vol. 1t77: Representation Theory I. Finite Dimensional Algebras. Edited by S. D. Comer. VI, 282 pages. 1985. Proceedings, t984. Edited by V. Dlab, P. Gabriel and G. Michler. XV, 340 pages. 1g86. Vol. 1150: B. Kawohl, Rearrangements and Convexity of Level Sets in Vol. 1178: Representation Theory II. Groups and Orders. Proceed­ PDE. V, 136 pages. 1985. ings, 1984. Edited by V. Dlab, P. Gabriel and G. Michler. XV, 370 Vol 1151: Ordinary and Partial Differential Equations. Proceedings, pages. 1986. 1984. Edited by B.D. Sleeman and R.J. Jarvis. XIV, 357 pages. 1985. Vol. 1179: Shi J .-Y. The Kazhdan-Lusztig Cells in Certain Affine Weyl Vol. 1152: H. Widom, Asymptotic Expansions for Pseudodifferential Groups. X, 307 pages. 1986. Operators on Bounded Domains. V, 150 pages. 1985. Vol. t180: R. Carmona, H. Kesten, J. B. Walsh, Ecole d'Ete de Vol. 1153: Probability in Banach Spaces V. Proceedings, 1984. Edited Probabilites de Saint-Flour XIV - 1984. Edite par P. L. Hennequin. X, by A. Beck, R. Dudley, M. Hahn, J. Kuelbs and M. Marcus. VI, 457 438 pages. 1986. pages. 1985. Vol. t181: Buildings and the Geometry of Diagrams, Como 1984. Vol. 1154: D. S. Naidu, A. K. Rao, Singular Pertubation Analysis of Seminar. Edited by L. Rosati. VII, 277 pages. 1986. Discrete Control Systems. IX, 195 pages. 1985. Vol. 1182: S. Shelah, Around Classification Theory of Models. VII, 279 Vol. 1155: Stability Problems for Stochastic Models. Proceedings, pages. 1986. 1984. Edited by V. V. Kalashnikov and V. M. Zolotarev. VI, 447 Vol. 1183: Algebra, Algebraic Topology and their Interactions. Procee­ pages. t985. dings, 1983. Edited by J.-E. Roos. XI, 396 pages. 1986. Vol. 1t56: Global Differential Geometry and Global Analysis 1984. Vol. 1184: W. Arendt, A. Grabosch, G. Greiner, U. Groh, H.P. Lotz, Proceedings, 1984. Edited by D. Ferus, R.B. Gardner, S. Helgason U. Moustakas, R. Nagel, F. Neubrander, U. Schlotterbeck, One­ and U. Simon. V, 339 pages. 1985. parameter Semigroups of Positive Operators. Edited by R. Nagel. X, 460 pages. 1986. Vol. 1t57: H. Levine, Classifying Immersions into!R4 over Stable Maps 2 of 3-Manifolds into!R • V, 163 pages. 1985. Vol. 1185: Group Theory, Beijing 1984. Proceedings. Edited by Tuan H. F. V, 403 pages. 1986. Vol. 1158: Stochastic Processes - Mathematics and Physics. Procee­ dings, t984. Edited by S. Albeverio, Ph. Blanchard and L. Streit. VI, Vol. 1t86: Lyapunov Exponents. Proceedings, 1984. Edited by L. 230 pages. t986. Arnold and V. Wihstutz. VI, 374 pages. 1986. Vol. t187: Y. Diers, Categories of Boolean Sheaves of Simple Vol. 1159: Schrodinger Operators, Como t984. Seminar. Edited by S. Algebras. VI, t68 pages. 1986. Graffi. VIII, 272 pages. 1986. Vol. 1188: Fonctions de Plusieurs Variables Complexes V. Seminaire, Vol. 1160: J.-C. van der Meer, The Hamiltonian Hopi Bifurcation. VI, 1979--85. Edite par Fran<;;ois Norguet. VI, 306 pages. 1986. t15 pages. 1985. Vol. 1t89: J. Lukes, J. Maly, L. Zajicek, Fine Topology Methods in Real Vol. 1161: Harmonic Mappings and Minimal Immersions, Montecatini Analysis and Potential Theory. X, 472 pages. t986. 1984. Seminar. Edited by E. Giusti. VII, 285 pages. Jg85. Vol. 1190: Optimization and Related Fields. Proceedings, 1984. Vol. 1162: S.J.L. van Eijndhoven, J. de Graaf, Trajectory Spaces, Edited by R. Conti, E. De Giorgi and F. Giannessi. VIII, 419 pages. IV, 272 pages. Generalized Functions and Unbounded Operators. t986. 1985. Vol. 1191: A.R. Its, V.Yu. Novokshenov, The lsomonodromic Defor­ Vol. 1163: Iteration Theory and its Functional Equations. Proceedings, Equations. IV, 313 pages. 1984. Edited by R. Liedl, L. Reich and Gy. Targonski. VIII, 23t pages. mation Method in the Theory of Painleve 1986. 1985. Vol. 1t92: Equadiff 6. Proceedings, t985. Edited by J. Vosmansky and Vol. 1164: M. Meschiari, J.H. Rawnsley, S. Salamon, Geometry M. Zlamal. XXIII, 404 pages. 1986. Seminar "Luigi Bianchi" II - 1984. Edrted by E. Vesentini. VI, 224 pages. 1985. Vol. t193: Geometrical and Statistical Aspects of Probability in Banach Spaces. Proceedings, t985. Edited by X. Femique, B. Vol. 1165: Seminar on Deformations. Proceedings, 1g82f84. Edited Heinkel, M.B. Marcus and P.A. Meyer. IV, 128 pages. t986. by J. -lawrynowicz. IX, 331 pages. 1985. Vol. 1194: Complex Analysis and Algebraic Geometry. Proceedings, Vol. 1166: Banach Spaces. Proceedings, 1984. Edited by N. Kalton 1985. Edited by H. Grauert. VI, 235 pages. t986. VI, 1g9 pages. 1g85. and E. Saab. Vol.t195: J.M. Barbosa, A. G. Colares, Mtnimal Surfaces in IRa X, t24 Vol. 1167: Geometry and Topology. Proceedings, 1983-84. Edited by pages. t986. J. Alexander and J. Harer. VI, 292 pages. 1985. Vol. tt96: E. Casas-Aivero, S. Xamb6-Descamps, The Enumerative Vol. 1168: S.S. Agaian, Hadamard Matric9s and their Applications. Ill, Theory of Conics after Halphen. IX, t30 pages. t986. 227 pages. 1985. Vol. t197: Ring Theory. Proceedings, t985. Edited by F.M.J. van Vol. 1169: W.A. Light, E.W. Cheney, Approximation Theory in Tensor Oystaeyen. V, 231 pages. t986. Product Spaces. VII, 157 pages. 1g95, Vol. 1198: Seminaire d'Analyse, P. Lelong- P. Dolbeau~- H. Skoda. Vol. 1170: B.S. Thomson, Real Functions. VII, 229 pages. 1985. Seminar 1983/84. X, 260 pages. 1986. Vol. 1171: Polynomes Orthogonaux et Applications. Proceedings, Vol. 1199: Analytic Theory of Continued Fractions II. Proceedings, 1984. Edite par C. Brezinski, A. Draux, A. P. Magnus, P. Maroni etA. 1985. Edited by W.J. Thron. VI, 299 pages. 1986. Ronveaux. XXXVII, 584 pages. 1985. Vol. 1200: V. D. Milman, G. Schechtman, Asymptotic Theory of Finite Vol. 1172: Algebraic Topology, Gottingen 1984. Proceedings. Edited Dimensional Normed Spaces. With an Appendix by M. Gromov. VIII, by L. Smith. VI, 209 pages. 1985. 156 pages. 1986. continued on page 45 7 Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann 1370 G. Carlsson R.L. Cohen H. R. Miller D.C. Ravenel (Eds.) Algebraic Topology Proceedings of an International Conference held in Arcata, California, July 27 - August 2, 1986 Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Editors Gunnar Carlsson Princeton University, Department of Mathematics Princeton, NJ 08544, USA Ralph Cohen Stanford University, Department of Mathematics Stanford, CA 94305, USA Haynes Miller Massachusetts Institute of Technology, Room 2-237 Cambridge, MA 02139, USA Douglas Ravenel University of Rochester, Department of Mathematics Rochester, NY 14620, USA Mathematics Subject Classification (1980): 55-06 ISBN 3-540-51118-0 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-51118-0 Springer-Verlag New York Berlin Heidelberg Thiswork is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1989 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 PREFACE An international conference on algebraic topology was held July 27 to August 2, 1986, at Humboldt State University in Arcata, California, prior to ICM86 in Berkeley. The conference served in part to celebrate the silver jubilee of the journal Topology, and the sixtieth birthday of Edgar H. Brown. It was supported by a grant from the National Science Foundation and a bequest from Pergammon Press, publishers of Topology. The Proceedings contain papers submitted by conference participants. All were refereed, and we take this occasion to thank the referees. We would also like to thank the staff of the Jolly Giant Conference Center for its assistance in organizing this conference. Gunnar Carlsson Ralph Cohen Haynes Miller Doug Ravenel CONTENTS James, I.M. Topology: Past. Present and Future 1 Whitehead, G. The Work of Edgar H. Brown, Jr. in Topology 10 Adem, A. Homology Representations of Finite Transformation Groups 15 Anick. D.J. Homotopy Exponents for Spaces of Category Two 24 Bendersky, M. On the Complex Bordism of Classifying Davis. D.M. Spaces 53 Berrick. A. J. On Equivariant Maps and Immersions of Real Randall. D. Projective spaces 57 Berstein. I. Cogroups which are not Suspensions Harper J.R. 63 Boyer.Ch.P. Instantons and Homotopy Mann. B.M 87 Brown, E.H. Jr. On Real Homotopy Theory Szczarba. R.H. 103 Cohen. F.R. Some Remarks on the Space 1m J Peterson, F.P. 117 Davis. D.M. A New Spectrum Related to 7-connected Mahowald. M. Cobordism 126 Davis. M.W. Aspherical Manifolds without Smooth or PL Hausmann, J.-C. Structure 135 Dwyer. W.G. Homology with Simplicial Coefficients Kan. D.M.
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