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This book contains a collection of articles summarizing together
the state of knowl- edge in a broad portion of modern homotopy
theory. These articles were assembled during 1998 and 1999, on the
occasion of an emphasis semester organized by the Centre de Recerca
Matematica (CRM) and its highlight, the 1998 Barcelona Con- ference
on Algebraic Topology (BCAT). First of all, we are indebted to all
the authors for submitting their work, and to the referees for
their help in the selec- tion and for their generous contribution
to the content of the articles. Many talks given during the CRM
semester or at the conference focused on aspects of the following
topics: abstract stable homotopy, model categories, homotopical
localizations and cellular approximations, p-compact groups, mod-
ules over the Steenrod algebra, classifying spaces for proper
actions of discrete groups, K-theory and other generalized
cohomology theories, cohomology of fi- nite and profinite groups,
Hochschild homology, configuration spaces, Lusternik- Schnirelmann
category, stable and unstable splittings. Other talks treated
multi- disciplinary subjects related to quantum field theory,
differential geometry, homo- topical dynamics, tilings, and various
aspects of group theory. In addition, an advanced course on
Classifying Spaces and Cohomology of Groups was organized by the
CRM in the days preceding the conference. Lecture notes from this
course will be published by Birkhauser Verlag as the first volume
of a newly created CRM Advanced Course series.
This book contains a collection of articles summarizing together
the state of knowl- edge in a broad portion of modern homotopy
theory. These articles were assembled during 1998 and 1999, on the
occasion of an emphasis semester organized by the Centre de Recerca
Matematica (CRM) and its highlight, the 1998 Barcelona Con- ference
on Algebraic Topology (BCAT). First of all, we are indebted to all
the authors for submitting their work, and to the referees for
their help in the selec- tion and for their generous contribution
to the content of the articles. Many talks given during the CRM
semester or at the conference focused on aspects of the following
topics: abstract stable homotopy, model categories, homotopical
localizations and cellular approximations, p-compact groups, mod-
ules over the Steenrod algebra, classifying spaces for proper
actions of discrete groups, K-theory and other generalized
cohomology theories, cohomology of fi- nite and profinite groups,
Hochschild homology, configuration spaces, Lusternik- Schnirelmann
category, stable and unstable splittings. Other talks treated
multi- disciplinary subjects related to quantum field theory,
differential geometry, homo- topical dynamics, tilings, and various
aspects of group theory. In addition, an advanced course on
Classifying Spaces and Cohomology of Groups was organized by the
CRM in the days preceding the conference. Lecture notes from this
course will be published by Birkhauser Verlag as the first volume
of a newly created CRM Advanced Course series.
The papers in this collection, all fully refereed, original papers,
reflect many aspects of recent significant advances in homotopy
theory and group cohomology. From the Contents: A. Adem: On the
geometry and cohomology of finite simple groups.- D.J. Benson:
Resolutions and Poincar duality for finite groups.- C. Broto and S.
Zarati: On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C.
Ravenel: Morava K-theories of classifying spaces and generalized
characters for finite groups.- K. Ishiguro: Classifying spaces of
compact simple lie groups and p-tori.- A.T. Lundell: Concise tables
of James numbers and some homotopyof classical Lie groups and
associated homogeneous spaces.- J.R. Martino: Anexample of a stable
splitting: the classifying space of the 4-dim unipotent group.-
J.E. McClure, L. Smith: On the homotopy uniqueness of BU(2) at the
prime 2.- G. Mislin: Cohomologically central elements and fusion in
groups.
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