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