Topological Topics: Articles on Algebra and Topology Presented to Professor P J Hilton in Celebration of his Sixtieth Birthday

192 Pages·1983·5.63 MB·English

by  I. M. James

LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES
Managing Editor: Professor I.M. James,
Mathematical Institute, 24-29 St Giles,Oxford
I. General cohomology theory and K-theory, P.HILTON
4. Algebraic topology, J.F.ADAMS
5. Commutative algebra, J.T.KNIGHT
8. Integration and harmonic analysis on compact groups, R.E.EDWARDS
9. Elliptic functions and elliptic curves, P.DU VAL
10. Numerical ranges II, F.F.BONSALL & J.DUNCAN
II. New developments in topology, G.SEGAL (ed.)
12. Symposium on complex analysis, Canterbury, 1973, J.CLUNIE
& W.K.HAYMAN (eds.)
13. Combinatorics: Proceedings of the British Combinatorial Conference
1973, T.P.McDONOUGH & V.C.MAVRON (eds.)
15. An introduction to topological groups, P.J.HIGGINS
16. Topics in finite groups, T.M.GAGEN
17. Differential germs and catastrophes, Th.BROCKER & L.LANDER
18. A geometric approach to homology theory, S.BUONCRISTIANO, C.P. ROURKE
& B.J.SANDERSON
20. Sheaf theory, B.R.TENNISON
21. Automatic continuity of linear operators, A.M.SINCLAIR
23. Parallelisms of complete designs, P.J.CAMERON
24. The topology of Stiefel manifolds, I.M.JAMES
25. Lie groups and compact groups, J.F.PRICE
26. Transformation groups: Proceedings of the conference in the University
of Newcastle-upon-Tyne, August 1976, C.KOSNIOWSKI
27. Skew field constructions, P.M.COHN
28. Brownian motion, Hardy spaces and bounded mean oscillations,
K.E.PETERSEN
29. Pontryagin duality and the structure of locally compact Abelian
groups, S.A.MORRIS
30. Interaction models, N.L.BIGGS
31. Continuous crossed products and type III von Neumann algebras,
A.VAN DAELE
32. Uniform algebras and Jensen measures, T.W.GAMELIN
33. Permutation groups and combinatorial structures, N.L.BIGGS & A.T.WHITE
34. Representation theory of Lie groups, M.F. ATIYAH et al.
35. Trace ideals and their applications, B.SIMON
36. Homological group theory, C.T.C.WALL (ed.)
37. Partially ordered rings and semi-algebraic geometry, G.W.BRUMFIEL
38. Surveys in combinatorics, B.BOLLOBAS (ed.)
39. Affine sets and affine groups, D.G.NORTHCOTT
40. Introduction to Hp spaces, P.J.KOOSIS
41. Theory and applications of Hopf bifurcation, B.D.HASSARD,
N.D.KAZARINOFF & Y-H.WAN
42. Topics in the theory of group presentations, D.L.JOHNSON
43. Graphs, codes and designs, P.J.CAMERON & J.H.VAN LINT
44. Z/2-homotopy theory, M.C.CRABB
45. Recursion theory: its generalisations and applications, F.R.DRAKE
& S.S.WAINER (eds.)
46. p-adic analysis: a short course on recent work, N.KOBLITZ
47. Coding the Universe, A.BELLER, R.JENSEN & P.WELCH
48. Low-dimensional topology, R.BROWN & T.L.THICKSTUN (eds.)
49. Finite geometries and designs, P.CAMERON, J.W.P.HIRSCHFELD
& D.R.HUGHES (eds.)
50. Commutator calculus and groups of homotopy classes, H.J.BAUES
51. Synthetic differential geometry, A.KOCK
52. Combinatorics, H.N.V.TEMPERLEY (ed.)
53. Singularity theory, V.I.ARNOLD
54. Markov processes and related problems of analysis, E.B.DYNKIN
55. Ordered permutation groups, A.M.W.GLASS
56. Journ£es arithmetiques 1980, J.V.ARMITAGE (ed.)
57. Techniques of geometric topology, R.A.FENN
58. Singularities of smooth functions and maps, J.MARTINET
59. Applicable differential geometry, M.CRAMPIN & F.A.E.PIRANI
60. Integrable systems, S.P.NOVIKOV et al.
61. The core model, A.DODD
62. Economics for mathematicians, J.W.S.CASSELS
63. Continuous semigroups in Banach algebras, A.M.SINCLAIR
64. Basic concepts of enriched category theory, G.M.KELLY
65. Several complex variables and complex manifolds I, M.J.FIELD
66. Several complex variables and complex manifolds II, M.J.FIELD
67. Classification problems in ergodic theory, W.PARRY & S.TUNCEL
68. Complex algebraic surfaces, A.BEAUVILLE
69. Representation theory, I.M.GELFAND et al.
70. Stochastic differential equations on manifolds, K.D.ELWORTHY
71. Groups - St Andrews 1981, C.M.CAMPBELL & E.F.ROBERTSON (eds.)
72. Commutative algebra: Durham 1981, R.Y.SHARP (ed.)
73. Riemann surfaces: a view towards several complex variables,
A.T.HUCKLEBERRY
74. Symmetric designs: an algebraic approach, E.S.LANDER
75. New geometric splittings of classical knots (algebraic knots),
L.SIEBENMANN & F.BONAHON
76. Linear differential operators, H.O.CORDES
77. Isolated singular points on complete intersections, E.J.N.LOOIJENGA
78. A primer on Riemann surfaces, A.F.BEARDON
79. Probability, statistics and analysis, J.F.C.KINGMAN & G.E.H.REUTER (eds.)
80. Introduction to the representation theory of compact and locally
compact groups, A.ROBERT
81. Skew fields, P.K.DRAXL
82. Surveys in combinatorics: Invited papers for the ninth British
Combinatorial Conference 1983, E.K.LLOYD (ed.)
83. Homogeneous structures on Riemannian manifolds, F.TRICERRI & L.VANHECKE
84. Finite group algebras and their modules, P.LANDROCK
85. Solitons, P.G.DRAZIN
86. Topological topics, I.M.JAMES (ed.)
87. Surveys in set theory, A.R.D.MATHIAS (ed.)
London Mathematical Society Lecture Note Series: 86
Topological Topics
Articles on algebra and topology presented to
Professor P.J. Hilton in celebration of his
sixtieth birthday
I.M. JAMES
Mathematical Institute, University of Oxford
CAMBRIDGE UNIVERSITY PRESS
Cambridge
London New York New Rochelle
Melbourne Sydney
Published by the Press Syndicate of the University of Cambridge
The Pitt Building, Trumpington Street, Cambridge CB2 1RP
32 East 57th Street, New York, NY 10022, USA
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©Cambridge University Press 1983
First published 1983
Library of Congress catalogue card number: 83-7745
British Library Cataloguing in Publication Data
Topological topics - (Lecture note series/London
Mathematical Society, ISSN 0076-0552; 86)
1. Topology - Addresses, essays, lectures
I. James, I.M. II. Hilton, P.J.
III. Series
514 QA611.15
ISBN 0 521 27581 4
Transferred to digital printing 2002
In honour of Peter Hilton
on the occasion of
his sixtieth birthday

CONTENTS
Publications of P.J. Hilton 1
Essay on Hilton's work in topology 15
Guido Mislin
The work of Peter Hilton in algebra 31
Urs Stammbach
The dual Whitehead theorems 46
J.P. May
Homotopy cocomplete classes of spaces and the 55
realization of the singular complex
D. Puppe
Betti numbers of Hilbert modular varieties 70
E. Thomas and A.T. Vasquez
Homotopy pairs in Eckmann-Hilton duality 88
K.A. Hardie
Profinite Chern classes for group representations 103
Beno Eckmann and Guido Mislin
Automorphisms of surfaces and class numbers: an 120
illustration of the G-index theorem
John Ewing
The real dimension of a vector bundle at the prime two 128
Edgar H, Brown, Jr. and Franklin P. Peterson
Maps between classifying spaces, III 136
J.F. Adams and Z. Mahmud
Idempotent codensity monads and the profinite completion 154
of topological groups
A. Deleanu
Finitary automorphisms and integral homology 164
J- Roitberg
Finite group actions on Grassman manifolds 169
Henry H. Glover and Guido Mislin

PUBLICATIONS OF P.J. HILTON
* Book
[l] Calculating the homotopy groups of A -polyhedra I, Quart. J.
Math. Oxford (2), 1 (1950), 299-309. n
[2] Calculating the homotopy groups of A -polyhedra II, Quart. J.
Math. Oxford (2), 2 (1951), 228-240. n
[3] Suspension theorems and the generalized Hopf invariant, Proc.
London Math. Soc. (3), 1 (1951), 462-493.
[4] The Hopf invariant and homotopy groups of spheres, Proc. Cambridge
Phil. Soc, 48 (1952), 547-554.
[5*] An introduction to homotopy theory, Cambridge University Press,
(1953).
[6] (with M.G. Barratt), On join operations in homotopy groups, Proc.
London Math. Soc. (3), 1 (1953), 430-445.
[7] (with J.H.C. Whitehead), Note on the Whitehead product, Ann. of
Math., 58 (1953), 429-442.
[8] On the Hopf invariant of a composition element, J. London Math.
Soc. 29 (1954), 165-171.
[9] A certain triple Whitehead product, Proc. Cambridge Phil. Soc,
50 (1954), 189-197.
[10] On the homotopy groups of the union of spheres, Proc. Int. Cong.
Amsterdam (1954).
[ll] On the homotopy groups of the union of spaces, Comment. Math.
Helv. 29 (1955), 59-92.
[12] Note on the P-homomorphism in homotopy groups of spheres, Proc.
Cambridge Phil. Soc. 51 (1955), 230-233.
[13] On the homotopy groups of the union of spheres, J. London
Math. Soc, 30 (1955), 154-172.
[14] Remark on the factorization of spaces, Bull. Acad. Polon. Sci.
(1) III. 3 (1955) 579-581.
[15] On Borsuk dependence and duality, Bull. Soc Math. Belg.,
7 (1955), 143-155.
[16] (with J.F. Adams), On the chain algebra of a loop space, Comment.
Math. Helv. 30 (1956), 305-330.
[17] Note on the higher Hopf invariants, Proc Cambridge Phil. Soc
52 (1956), 750-752.
[18] Remark on the tensor product of modules, Bull.Acad. Polon. Sci.
Cl. III., 4 (1956), 325-328.
[19] Generalizations of the Hopf invariant, Colloque de Topologie Al-
gebrique, C.B.R.M. (1956), 9-27.
Publications of P.J. Hilton 2
[20] Note on quasi Lie rings, Fund. Math. 43 (1956), 203-237.
[2l] On divisors and multiples of continuous maps, Fund. Math. 43
(1957), 358-386.
[22] (with W. Ledermann) Homology and ringoids I, Proc. Cambridge
Phil. Soc, 54 (1958), 152-167.
[23] (with B. Eckmann) Groupes d'homotopie et dualite. Groupes absolus,
C.R. Acad. Sci. Paris, 246 (1958), 2444-2447.
[24] (with B. Eckmann) Groupes d'homotopie et dualite. Suites exactes,
C.R. Acad. Sci. Paris, 246 (1958), 2555-2558.
[25] (with B. Eckmann) Groupes d'homotopie et dualite. Coefficients,
C.R. Acad. Sci. Paris, 246 (1958), 2991-2993.
[26] (with B. Eckmann) Transgression homotopique et cohomologique,
C.R. Acad. Sci. Paris, 247 (1958), 629-632.
[27] (with W. Ledermann) Homological ringoids, Coll.Math. 6 (1958),
177-186.
[28*] Differential calculus, Routledge and Kegan Paul, (1958).
[29] (with B. Eckmann) Decomposition homologique d'un polyedre simple-
ment connexe, C.R. Acad. Sci. Paris, 248 (1959), 2054-2056.
[30] (with B. Eckmann) Homology and homotopy decomposition of con-
tinuous maps, Proc. Nat. Acad. Sci., 45 (1959), 372-375.
[31] Homotopy theory of modules and duality, Proc. Mexico Symposium,
(1958), 273-281.
[32] (with W. Ledermann) Homology and ringoids II, Proc. Cambridge
Phil. Soc. 55 (1959), 129-164.
[33] (with T. Ganea) Decomposition of spaces in cartesian products
and unions, Proc. Cambridge Phil. Soc, 55 (1959), 248-256.
[34] (with W. Ledermann) Homology and ringoids III, Proc. Cambridge
Phil. Soc, 56 (1960), 1-12.
[35] (with W. Ledermann) On the Jordan-Holder theorem in homological
monoids, Proc London Math. Soc (3), 10 (1960), 321-334.
[36] On an generalization of nilpotency to semi-simplicial complexes,
Proc London Math. Soc (3), 10 (1960), 604-622.
[37] (with B. Eckmann) Operators and co-operators in homotopy theory,
Math. Ann. 141 (1960), 1-21.
[38] (with I. Berstein) Category and generalized Hopf invariants, 111.
J. Math., 4 (1960), 437-451.
[39*] Partial derivatives, Routledge and Kegan Paul, (1960).
[40*] (with S. Wylie) Homology Theory, Cambridge Univ. Press, (1960).
[41] (with E.H. Spanier) On the embeddability of certain complexes in
Euclidean spaces, Proc. Amer. Math. Soc, 11 (1960), 523-526.
[42] Remark on the free product of groups, Trans. Amer. Math. Soc, 96
(1960), 478-488.