Homology, Homotopy and Applications

Volume 1 (1999)

1. Groupoids and crossed objects in algebraic topology Ronald Brown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–78

2. A homotopy 2-groupoid from a fibration K.H. Kamps and T. Porter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79–93

3. The Boardman Category of spectra, Chain complexes and (Co-)Localizations Friedrich W. Bauer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95–116

4. Higher Homotopy Groupoids and Toda Brackets K.A. Hardie, K.H. Kamps and R.W. Kieboom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117–134

5. K-theory of affine toric varieties Joseph Gubeladze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135–145

6. A Categorical Guide to Separation, Compactness and Perfectness Walter Tholen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147–161

7. Computing Second Cohomology of Finite Groups with Trivial Coefficients Graham Ellis and Irina Kholodna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163–168

8. Operations and Quantum Doubles in Complex Oriented Cohomology Theory Victor M. Buchstaber and Nigel Ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169–185

9. Non-abelian tensor and exterior products modulo q and universal q-central relative extension of Lie algebras Emzar Khmaladze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187–204

10. On spaces of the same strong n-types Yves Flix and Jean-Claude Thomas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205–217

Homology, Homotopy and Applications (ISSN 1512 - 0139) is the all-electronic, refereed journal on Homological and Homotopical Algebra and their applications in the mathematical sciences.

The influence of homology and homotopy is found in many fundamental domains of mathematics and the aim of “Homology, Homotopy and Applications” is to unify such applications, to show its merit, importance and diversity and to present in time to its reader new information about the progress of the area and the relationships with other fields.

To this end “Homology, Homotopy and Applications” will publish carefully refereed significant and original research papers and expository survey papers of high level in the area, as well as research papers having substantial applications of results and technique of homological and homotopical algebra, for example to general algebra, algebraic topology, algebraic homotopy, algebraic geometry, K-theory, category theory,computer science, Galois theory, functional analysis, algebraic number theory, differential geometry and topology.

Articles appearing in the journal have been carefully and critically refereed under the responsibility of members of the Editorial Board. Only papers judged excellent are accepted for publication.

The method of distribution of the journal is via Internet tools (WWW, ftp, etc.)

The journal is archived electronically and in printed paper format.

Subscribers to the journal receive abstracts of accepted papers by electronic mail. Compiled TEX(.dvi) and Postscript files of the full articles are available by WWW/ftp.

The journal is free to individuals.

University Departments, Libraries, and other institutional subscribers are invited to consult with the Editor-in-Chief about subscription and archiving. Authors retain copyright to articles appearing in the Journal. The Journal is copyrighted by its Editorial Board. For further information, contact the Editor-in-Chief, Hvedri Inassaridze, hvedri@rmi.acnet.ge.

Homology, Homotopy and Applications uses the TEXtypesetting system to define its contents and the Internet to disseminate them. Authors are invited to submit articles to any member of the Editorial Board and the Editor-in-Chief in any standard flavour of TEX(i.e. plain, L^{A}TEX, AMS-(La) TEX.). Tex sorces files may be submitted by email directly to only one member of the Editorial Board.

Accepted papers will be archived electronically in DVI and Postscript format by the journal. A printed paper version of each article in the journal is archived in the Razmadze Mathematical Institute library.

EDITORIAL BOARD

Editor-in-Chief:

Hvedri Inassaridze, A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Alexidze Str.1, Tbilisi 380093, Georgia.

hvedri@rmi.acnet.ge    hvedri.inassari@usa.net

Managing Editors:

Ronald Brown, University of North Wales, UK: r.brown@bangor.ac.uk J. Nigel Ray, University of Manchester, UK: nige@ma.man.ac.uk Lionel Schwartz, Universit de Paris 13, France: schwartz@math.univ-paris13.fr

Editors:

Luchezar Avramov, Purdue University, USA: avramov@Math.Purdue.Edu Michael Barr, McGill University, Canada: barr@triples.math.mcgill.ca Lawrence Breen, Universite de Paris 13, France: breen@math.univ-paris13.fr Winfried Bruns, Universitt Osnabrck, Germany: winfried@mathematik.Uni-Osnabrueck.de Aurelio Carboni, University of Insubria, Italy: acarboni@mailserver.unimi.it Antonio Martinez Cegarra, University of Granada, Spain: acegarra@goliat.ugr.es Claude Cibils, University of Montpellier, France. cibils@math.univ-montp2.fr R. Keith Dennis, Cornell University, Ithaca, USA: rkd@ams.org, dennis@math.cornell.edu Graham Ellis, University College of Galway, Ireland: Graham.Ellis@ucg.ie Daniel Guin, University of Montpellier, France dguin@math.univ-montp2.fr Jürgen Herzog, Universität GH Essen, Germany: mat300@uni-essen.de Johannes Hbschmann, Universit de Lille, France: Huebschmann@Univ-Lille1.fr G. Max Kelly, University of Sydney, Australia: maxk@maths.usyd.edu.au Frans Keune, University of Nijmegen, The Netherlands: keune@sci.kun.nl Larry Lambe, University of Stockholm, Sweden: lambe@matematik.su.se Jean-Louis Loday, Universit de Strasbourg, France: loday@math.u-strasbg.fr Andy R. Magid, University of Oklahoma, USA: amagid@uoknor.edu Wolfgang Metzler, University of Frankfurt, Germany metzler@math.uni-frankfurt.de Alexander Mishchenko, Moscow State University, Russia asmish@mech.math.msu.su Shigeyuki Morita, University of Tokyo, Japan: morita@ms.u-tokyo.ac.jp Maria Cristina Pedicchio, University of Trieste, Italy: pedicchi@uts.univ.trieste.it Ulf Rehmann, University of Bielefeld, Germany: rehmann@mathematik.uni-bielefeld.de Jonathan M. Rosenberg, University of Maryland, USA: jmr@math.umd.edu Andrea Solotar, University of Buenos Aires, Argentina asolotar@dm.uba.ar,

                                   asolotar@topo.math.u-psud.fr

James Stasheff, University of North Carolina, USA: jds@math.unc.edu Ross Street, Macquarie University, Australia: street@macadam.mpce.mq.edu.au Tomohide Terasoma, University of Tokyo, Japan terasoma@gauss.ms.u-tokyo.ac.jp Walter Tholen, York University, Canada: tholen@mathstat.yorku.ca Charles A. Weibel, Rutgers University, New Brunswick, USA: weibel@euler.rutgers.edu