Homology, Homotopy and Applications

Volume 2 (2000)

1. Stripping and conjugation in the mod p Steenrod algebra and its dual Dagmar M. Meyer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–16

2. Truncations of the ring of number-theoretic functions Jan Snellman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17–27

3. On the cohomology of some Hopf algebroids and Hattori-Stong theorems Andrew Baker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29–40

4. The low-dimensional homology of crossed modules N D Gilbert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41–50

5. Homological Perturbation Theory and Associativity Pedro Real . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51–88

6. Continuous family groupoids Alan L. T. Paterson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89–104

7. More about homological Properties of precrossed modules Nick Inassaridze and Emzar Khmaladze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105–114

8. Erratum to ”On spaces of the same strong n-type”

[HHA, v. 1 (1999) No. 10, pp. 205-217] Yves Fèlix and Jean-Claude Thomas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115–118

9. Topological K-theory of the Integers at the Prime 2 Luke Hodgkin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119–126

10. KK-theory as the K-theory of C^{∗}-categories Tamaz Kandelaki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127–145

11. On the Freyd Categories of an Additive Category Apostolos Beligiannis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147–185

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

Editors-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

Gunnar Carlsson, University of Stanford, USA

gunnar@math.stanford.edu

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

Ralph Cohen, Stanford University, USA:

    ralph@math.stanford.edu

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 Hübschmann, Université 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

R. James Milgram, Stanford University, USA:

milgram@math.stanford.edu

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