Lecture Notes in Mathematics
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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. 143
Gray, B. On the Double Suspension 150
Hardie. K.A. A Whitehead Product for Track Groups Jansen, A.V. 163
Hopkins. M.J. Minimal Atlases for Real Projective Spaces 171
1wase. N. Higher Homotopy Associativity Mimura. M. 193
Jackowski. S. Homotopy Approximations for Classifying McClure. J.E. Spaces of Compact Lie Groups 221 v
Karoubi, M. Cyclic Homology and Characteristic Classes of Bundles with Additional Structures 235
Kuhn, N.J. Morava K-Theories and Infinite Loop Spaces 243
Lin, J.P. Lie Groups from a Homotopy Point of View 258
Lin, W.-H. Order of the Identity Map of the Brown- Gitler spectrum 274
L6pez de Topology of the Intersection of Quadrics Medrano, S. in Rn 280
Milgram, J.R. Orientations for Poincare Duality Spaces and Applications 293
MitchelL S.A. A Double Coset Pormula for Levi Subgroups Priddy, S.B. and Splitting BGL 325 n Morava, J. Browder-Prohlich Symbols 335
Pedersen, E.K. K-theory Homology of Spaces Weibel, Ch.A. 346
Ray, N. Stirling and Bernoulli Numbers for Complex Oriented Homology Theory 362
Robinson, A. Composition Products in RHom. and Ring Spectra of Derived Endomorphisms 374
Stark, Ch.W. Convexity and Root Closure in Negatively Curved Manifolds 387
Tezuka, M. Cohomology of Pinite Groups and Brown- Yagita, N. Peterson Cohomology 396 tom Dieck, T. The Artin-Hasse Logarithm for A-Rings 409
Zhou, X. Higher Cohomology Operations that Detect Homotopy Classes 416
Problem Session 437
Homotopy Theory (J.P. Adams) 438
H-Spaces 444
K and L Theory 446
Manifolds and Bordism 448
Transformation Groups 450
1. loan M. James, University of Oxford 2. James F. Davis, Indiana University 3. J. M. Boardman, Johns Hopkins University 4. Robert Bruner, Wayne State University 5. Michishige Tesuka, Tokyo Institute of Technology 6. John W. Wood, University of Illinois at Chicago 7. William M. Singer, Fordham University 8. Stanley O. Kochman, York University 9. Ronnie Lee, Yale University 10. Elias Micha, Centro del I.P.N., Mexico 11. 12. Anthony Bak, Universitat Bielefeld 13. John C. Harris, University of Washington 14. Michael J. Hopkins, Princeton University 15. Wilberd van der Kallen, State University of Utrecht 16. Masana Harada, Kyoto University 17. Thomas P. Bisson, Canisius College 18. Peter N. Hoffman, University of Waterloo 19. Uwe G. M. Hommel, University of Chicago 20. Larry R. Taylor, University of Notre Dame 2l. Alan C. Robinson, University of Warwick 22. Hirotaka Tarnanoi, Institute for Advanced Study 23. David Grayson, University of Illinois at Urbana-Champaign 24. Hans J. Munkholm, Odense Universitet 25. Max Karoubi, Universite Paris VII 26. James P. Lin, University of California at San Diego 27. Howard Marcum, Ohio State University 28. Eddy Campbell, Queen's University 29. Masaharu Morimoto, Okayama University 30. Paul L. Shick, John Carroll University 3l. Masatsugu Nagata, University of Chicago 32. Jack Wagoner, University of California at Berkeley 33. Peter B. Gilkey, University of Oregon 34. Steven A. Mitchell, University of Washington 35. Frank Williams, New Mexico State University 36. Gunnar Carlsson, Princeton University 37. David C. Johnson, University of Kentucky 38. Brayton <;'hay, University of Illinois at Chicago 39. Carlos Prieto, U.N.A.M., MeXICO 40. Thomas Goodwillie, Brown University 41. Keith P. Johnson, Dalhousie University 42. James E. West, Cornell University 43. Bruce Hughes, Vanderbilt University 44. Eldon Dyer, Grad. School and University Center, CUNY 45. Santiago Lopez de Medrano, U.N.A.M., Mexico 46. Kent E. Orr Brandeis University 47. Ralph L. Cohen, Stanford University 48. Douglas R. Anderson, Syracuse University VIII
49. Ross E. Staffeldt, Pennsylvania State University 50. J. Peter May, University of Chicago 51. Bruce Williams, University of Notre Dame 52. Monica Nicolau, University of California, Berkeley 53. Ethan S. Devinatz, University of Chicago 54. L. Gaunce Lewis, Jr., Syracuse University 55. Edgar H. Brown, Brandeis University 56. Nicholas J. Kuhn, University of Virginia 57. Arunas L. Liulevicius, University of Chicago 58. James A Schafer, University of Maryland 59. Kenshi Ishiguro, University of Chicago 60. 61. Edwin H. Spanier University of California at Berkeley 62. Charles A. Weibei , Rutgers University 63. Reinhard C. Laubenbacher, New Mexico State University 64. George W. Whitehead, Massachusetts Institute of Technology 65. Nobuaki Yagita, Masashi Institute of Technology 66. J. Frank Adams, University of Cambridge 67. Mark Feshbach, University of Minnesota 68. Jeremy H. C. Gunawardena, University of Cambridge 69. Keith A. Hardie, University of Cape Town 70. Benjamin M. Mann, Clarkson University 71. Richard Miranda 72. Daniel Miranda 73. Clarence W. Wilkerson, Wayne State University 74. Douglas C. Ravenel, University of Washington 75. Robert H. Szczarba, Yale University 76 John H. Ewing, Indiana University 77. A. Jon Berrick, National University of Singapore 78. Donald M. Davis, Lehigh University 79. Mark E. Mahowald, Northwestern University BO. Pierre Vogel, Universite de Nantes 81. Don H. Shimamoto, Swarthmore College 82. Dan Burghelea, Ohio State University 83. James E. McClure, University of Kentucky 84. Johan L. Dupont, University of Aarhus 85. Vietor P. Snaith, University of Western Ontario 86. Mamoru Mimura, Okayama University 87. Lionel Schwartz, Universite Paris-Sud 88. John H. McCleary, Vassar College 89. David J. Pengelley, New Mexico State University 90. John R. Harper, University of Rochester 91. Matthias Kreck, Johannes Gutenberg University 92. F. Thomas Farrell, Columbia University 93. Jean Lannes, Ecole Polytechnique 94. Roderick D. Ball, New Mexico State University 95. Nathan B. Habegger, University of California at San Diego 96. Haynes R. Miller, Massachusetts Institute of Technology IX
97. David J. Aniek, Massachusetts Institute of Technology 98. Frederick R. Cohen, University of Kentucky 99. Alexander E. Koonce, Yale University 100. Kaoru Morisugi, Wakayama University 101. Christopher W. Stark, University of Florida 102. Jean-Claude R. Hausmann, University of Geneva 103. Robert A. Oliver, Aarhus University 104. Andrew Niess, University of Toronto 105. Samuel Gitler, University of Rochester 106. Alexander Zabrodsky, Hebrew University 107. R. JamE!S Milgram, Stanford University 108. Remy Croisille, Ecole Normale Superieure 109. Francis X. Connolly, University of Notre Dame 110. 111. Wu-Chung Hsiang, Princeton University 112. William G. Dwyer, University of Notre Dame 113. Jeanne Duflot Colorado State University 114. Toshio Kawashima, Ashikaga Institute of Technology 115. Wen-Hsiung Lin, National Hua University 116. William Browder l Princeton University, 117. Hitoshi Moriyoshi, University of Tokyo 118. Enric Frau, Massachusetts Institute of Technology 119. Hiroo Shiga, Ryukyu University 120. Graham J. Ellis, University of North Wales 121. Norio Iwase, Kyushu University 122. Marcelo A. Aguilar, U.N.A.M., Mexico 123. Jerry M. Lodder, Stanford University 124. Norihiko Minami, Northwestern University 125. Aleksandar Vucic, University of Washington 126. Alexander Adem, Stanford University 127. Francis Clarke, University College, Swansea 128. Stefan Jackowski, University of Warsaw 129. Tsuneyo Yamanoshita; Masashi Institute of Technology 130. John Scott Maginnis, Stanford University 131. Nigel Ra.y, Manchester University 132. Stewart R. Priddy, Northwestern University 133. Noriko Minami 134. Tammo tom Dieck, Gottingen 135. Mikio Furuta, University of Tokyo 136. Henry H. Glover, Ohio State University 137. Zhou, Nankai University 138. DaVId Benson, University of Oxford 139. Georgia Triantafillou, University of Crete 140. Frank Quinn, Virginia Polytechnic Institute 141. Franklin P. Peterson, Massachusetts Institute of Technology 142. Peter A. Symonds, Ohio State University 143. Ruth M. Charney, Ohio State University 144. Luisa Avez, University of Rochester 145. Joseph A. Neisendorfer, University of Rochester 146. Martin C. Tangora, University of Illinois at Chicago