**Contemporary Mathematics**

Volume: 274;
2001;
315 pp;
Softcover

MSC: Primary 55;

Print ISBN: 978-0-8218-2683-6

Product Code: CONM/274

List Price: $96.00

Individual Member Price: $76.80

**Electronic ISBN: 978-0-8218-7864-4
Product Code: CONM/274.E**

List Price: $96.00

Individual Member Price: $76.80

# Groups of Homotopy Self-Equivalences and Related Topics

Share this page *Edited by *
*Ken-ichi Maruyama; John W. Rutter*

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.

#### Table of Contents

# Table of Contents

## Groups of Homotopy Self-Equivalences and Related Topics

- Contents vii8 free
- Foreword ix10 free
- Homotopy self-equivalences 1988–1999 112 free
- Bibliography on ε(X) 1988–1999 1324
- Subgroups of the group of self-homotopy equivalences 2132
- The space of free loops on a real projective space 3344
- Indecomposable homotopy types with at most two non-trivial homology groups 3950
- Square rings associated to elements in homotopy groups of spheres 5768
- Fibrations with product of Eilenberg-MacLane space fibres I 7990
- Self homotopy equivalences of equivariant spheres 105116
- Two examples to illustrate properties of the group of self-equivalences of a finite CW complex X 133144
- Nilpotency and localization of groups of fibre homotopy equivalences 145156
- The homotopy groups of the homotopy fibre of an induced map of function spaces 159170
- Fibrations, self homotopy equivalences and negative derivations 169180
- Classifying spaces and a subgroup of the exceptional Lie group G2 183194
- The structure of the Hurewicz homomorphism 195206
- Joins, diagonals and Hopf invariants 203214
- A subgroup of self homotopy equivalences which is invariant on genus 225236
- Composition structure of the self-maps of SU(3) or Sp(2) 233244
- Self-homotopy of a suspension of the real 4-projective space 241252
- Phantom elements and its applications 257268
- Homotopy equivalences of lens spaces of one-relator groups 269280
- Principal S1-bundles and forgetful maps 293304
- Rational type of classifying spaces for fibrations 299310
- Problems on self-homotopy equivalences 309320

#### Readership

Graduate students and research mathematicians interested in algebraic topology.