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Book DetailsContemporary MathematicsVolume: 274; 2001; 315 ppMSC: Primary 55;
This volume offers the proceedings from the workshop held at the Gargnano Institute of the University of Milan (Italy) on groups of homotopy selfequivalences and related topics. The book comprises articles of current research on the group of homotopy selfequivalences, 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 speciallywritten articles, by J. W. Rutter, reviewing the work done in the area of homotopy selfequivalences 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.ReadershipGraduate students and research mathematicians interested in algebraic topology.

Table of Contents

Articles

John W. Rutter  Homotopy selfequivalences 1988–1999 [ MR 1816998 ]

John W. Rutter  Bibliography on $\scr E(X)$ 1988–1999 [ MR 1816999 ]

Martin Arkowitz, Gregory Lupton and Aniceto Murillo  Subgroups of the group of selfhomotopy equivalences [ MR 1817000 ]

Sven Bauer, Michael Crabb and Mauro Spreafico  The space of free loops on a real projective space [ MR 1817001 ]

HansJoachim Baues and Yuri Drozd  Indecomposable homotopy types with at most two nontrivial homology groups [ MR 1817002 ]

HansJoachim Baues and Norio Iwase  Square rings associated to elements in homotopy groups of spheres [ MR 1817003 ]

Peter I. Booth  Fibrations with product of EilenbergMacLane space fibres. I [ MR 1817004 ]

Davide L. Ferrario  Self homotopy equivalences of equivariant spheres [ MR 1817005 ]

Y. Felix  Two examples to illustrate properties of the group of selfequivalences of a finite CW complex $X$ [ MR 1817006 ]

A. Garvín, A. Murillo, P. Pavešić and A. Viruel  Nilpotency and localization of groups of fibre homotopy equivalences [ MR 1817007 ]

K. A. Hardie and K. H. Kamps  The homotopy groups of the homotopy fibre of an induced map of function spaces [ MR 1817008 ]

Volker Hauschild  Fibrations, self homotopy equivalences and negative derivations [ MR 1817009 ]

Kenshi Ishiguro  Classifying spaces and a subgroup of the exceptional Lie group $G_2$ [ MR 1817010 ]

Donald Kahn and Christopher Schwartz  The structure of the Hurewicz homomorphism [ MR 1817011 ]

Howard J. Marcum  Joins, diagonals and Hopf invariants [ MR 1817012 ]

Kenichi Maruyama  A subgroup of self homotopy equivalences which is invariant on genus [ MR 1817013 ]

Kaoru Morisugi  Composition structure of the self maps of $\rm SU(3)$ or $\rm Sp(2)$ [ MR 1817014 ]

Juno Mukai  Selfhomotopy of a suspension of the real 4projective space [ MR 1817015 ]

Jianzhong Pan and Moo Ha Woo  Phantom elements and its applications [ MR 1817016 ]

John W. Rutter  Homotopy equivalences of lens spaces of onerelator groups [ MR 1817017 ]

H. Shiga, K. Tsukiyama and T. Yamaguchi  Principal $S^1$bundles and forgetful maps [ MR 1817018 ]

Samuel Bruce Smith  Rational type of classifying spaces for fibrations [ MR 1817019 ]

Martin Arkowitz  Problems on SelfHomotopy Equivalences


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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 selfequivalences and related topics. The book comprises articles of current research on the group of homotopy selfequivalences, 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 speciallywritten articles, by J. W. Rutter, reviewing the work done in the area of homotopy selfequivalences 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.

Articles

John W. Rutter  Homotopy selfequivalences 1988–1999 [ MR 1816998 ]

John W. Rutter  Bibliography on $\scr E(X)$ 1988–1999 [ MR 1816999 ]

Martin Arkowitz, Gregory Lupton and Aniceto Murillo  Subgroups of the group of selfhomotopy equivalences [ MR 1817000 ]

Sven Bauer, Michael Crabb and Mauro Spreafico  The space of free loops on a real projective space [ MR 1817001 ]

HansJoachim Baues and Yuri Drozd  Indecomposable homotopy types with at most two nontrivial homology groups [ MR 1817002 ]

HansJoachim Baues and Norio Iwase  Square rings associated to elements in homotopy groups of spheres [ MR 1817003 ]

Peter I. Booth  Fibrations with product of EilenbergMacLane space fibres. I [ MR 1817004 ]

Davide L. Ferrario  Self homotopy equivalences of equivariant spheres [ MR 1817005 ]

Y. Felix  Two examples to illustrate properties of the group of selfequivalences of a finite CW complex $X$ [ MR 1817006 ]

A. Garvín, A. Murillo, P. Pavešić and A. Viruel  Nilpotency and localization of groups of fibre homotopy equivalences [ MR 1817007 ]

K. A. Hardie and K. H. Kamps  The homotopy groups of the homotopy fibre of an induced map of function spaces [ MR 1817008 ]

Volker Hauschild  Fibrations, self homotopy equivalences and negative derivations [ MR 1817009 ]

Kenshi Ishiguro  Classifying spaces and a subgroup of the exceptional Lie group $G_2$ [ MR 1817010 ]

Donald Kahn and Christopher Schwartz  The structure of the Hurewicz homomorphism [ MR 1817011 ]

Howard J. Marcum  Joins, diagonals and Hopf invariants [ MR 1817012 ]

Kenichi Maruyama  A subgroup of self homotopy equivalences which is invariant on genus [ MR 1817013 ]

Kaoru Morisugi  Composition structure of the self maps of $\rm SU(3)$ or $\rm Sp(2)$ [ MR 1817014 ]

Juno Mukai  Selfhomotopy of a suspension of the real 4projective space [ MR 1817015 ]

Jianzhong Pan and Moo Ha Woo  Phantom elements and its applications [ MR 1817016 ]

John W. Rutter  Homotopy equivalences of lens spaces of onerelator groups [ MR 1817017 ]

H. Shiga, K. Tsukiyama and T. Yamaguchi  Principal $S^1$bundles and forgetful maps [ MR 1817018 ]

Samuel Bruce Smith  Rational type of classifying spaces for fibrations [ MR 1817019 ]

Martin Arkowitz  Problems on SelfHomotopy Equivalences