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Groups of Homotopy Self-Equivalences and Related Topics
Edited by: Ken-ichi Maruyama, Chiba University, Japan, and John W. Rutter, University of Liverpool, England

Contemporary Mathematics
2001; 315 pp; softcover
Volume: 274
ISBN-10: 0-8218-2683-2
ISBN-13: 978-0-8218-2683-6
List Price: US$91
Member Price: US$72.80
Order Code: CONM/274
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This volume offers the proceedings from the workshop held at the Gargnano Institute of the University of Milan (Italy) on groups of homotopy self-equivalences and related topics. The book comprises articles of current research on the group of homotopy self-equivalences, the homotopy of function spaces, rational homotopy theory, the classification of homotopy types, and equivariant homotopy theory.

Mathematicians from many areas of the globe attended the workshops to discuss their research and to share ideas. Included are two specially-written articles, by J. W. Rutter, reviewing the work done in the area of homotopy self-equivalences since 1988. Included also is a bibliography of some 122 articles published since 1988 and a list of problems. This book is suitable for both advanced graduate students and researchers.


Graduate students and research mathematicians interested in algebraic topology.

Table of Contents

  • J. W. Rutter -- Homotopy self-equivalences 1988-1999
  • J. W. Rutter -- Bibliography on \(\mathcal E(X)\) 1988-1999
  • M. Arkowitz, G. Lupton, and A. Murillo -- Subgroups of the group of self-homotopy equivalences
  • S. Bauer, M. Crabb, and M. Spreafico -- The space of free loops on a real projective space
  • H.-J. Baues and Y. Drozd -- Indecomposable homotopy types with at most two non-trivial homology groups
  • H.-J. Baues and N. Iwase -- Square rings associated to elements in homotopy groups of spheres
  • P. I. Booth -- Fibrations with product of Eilenberg-MacLane space fibres I
  • D. L. Ferrario -- Self homotopy equivalences of equivariant spheres
  • Y. Felix -- Two examples to illustrate properties of the group of self-equivalences of a finite CW complex \(X\)
  • A. Garvín, A. Murillo, P. Pavešić, and A. Viruel -- Nilpotency and localization of groups of fibre homotopy equivalences
  • K. A. Hardie and K. H. Kamps -- The homotopy groups of the homotopy fibre of an induced map of function spaces
  • V. Hauschild -- Fibrations, self homotopy equivalences and negative derivations
  • K. Ishiguro -- Classifying spaces and a subgroup of the exceptional Lie group \(G_2\)
  • D. Kahn and C. Schwartz -- The structure of the Hurewicz homomorphism
  • H. J. Marcum -- Joins, diagonals and Hopf invariants
  • K.-i. Maruyama -- A subgroup of self homotopy equivalences which is invariant on genus
  • K. Morisugi -- Composition structure of the self maps of \(SU(3)\) or \(Sp(2)\)
  • J. Mukai -- Self-homotopy of a suspension of the real 4-projective space
  • J. Pan and M. H. Woo -- Phantom elements and its applications
  • J. W. Rutter -- Homotopy equivalences of lens spaces of one-relator groups
  • H. Shiga, K. Tsukiyama, and T. Yamaguchi -- Principal \(S^1\)-bundles and forgetful maps
  • S. B. Smith -- Rational type of classifying spaces for fibrations
  • M. Arkowitz -- Problems on self-homotopy equivalences
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