Homology, Homotopy and Applications

Volume 5(2), 2003

1. Introduction Gunnar Carlsson, Rick Jardine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

2. Dicovering spaces Lisbeth Fajstrup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–17

3. Computing Linking Numbers of a Filtration Herbert Edelsbrunner and Afra Zomorodian . . . . . . . . . . . . . . . . . . . . . . . . . 19–37

4. Topological Deformation of Higher Dimensional Automata Philippe Gaucher and Eric Goubault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39–82

5. Computation of Cohomology Operations on Finite Simplicial Complexes R. González–Díaz and P. Real . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83–93

6. Some Geometric Perspectives in Concurrency Theory Eric Goubault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95–136

7. On the Geometry of Intuitionistic S4 Proofs Jean Goubault-Larrecq and Eric Goubault . . . . . . . . . . . . . . . . . . . . . . . . 137–209

8. Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency Marco Grandis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211–231

9. Computing Homology Tomasz Kaczynski, Konstantin Mischaikow and Marian Mrozek … 233–256

10. State spaces and dipaths up to dihomotopy Martin Raussen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257–280

Homology, Homotopy and Applications (ISSN 1512 - 0139) is the all-electronic, refereed journal on homology and homotopy in algenra and their applications to the mathematical sciences. A printed version is published in partnership with ”International Press”, P.O. Box 43502, Somerville, MA 02143, USA, http://www.intlpress.com.

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), Postscript and .pdf 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 TEX typesetting 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 Editors-in-Chief in any standard flavour of TEX (i.e. plain, L^{A}TEX, AMS-(La) TEX.). Tex sources files may be submitted by email directly to only one member of the Editorial Board.

Accepted papers will be archived electronically in DVI, Postscript and PDF format by the journal.

EDITORIAL BOARD

Editors-in-Chief:

Hvedri Inassaridze, A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Alexidze Str.1, Tbilisi 0193, Georgia.

hvedri@rmi.acnet.ge

Gunnar Carlsson, University of Stanford, USA

gunnar@math.stanford.edu

Managing Editor:

Donald Davis, Lehigh University, USA: dmd1@lehigh.edu

Editors:

Dominique Arlettaz, University of Lausanne, Switzerland:

    dominique.arlettaz@ima.unil.ch

Luchezar Avramov, Purdue University, USA:

    avramov@Math.Purdue.Edu

Andrew Baker, University of Glasgow, UK:

    a.baker@maths.gla.ac.uk

Michael Barr, McGill University, Canada:

    barr@triples.math.mcgill.ca

Ronald Brown, University of North Wales, UK:

    r.brown@bangor.ac.uk

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

Benoit Fresse, University of Nice-Sophia-Antipolis, France:

    fresse@math1.unice.fr

Daniel Grayson, University of Illinois at Urbana-Champaign, USA:

    dan@math.uiuc.edu

Daniel Guin, University of Montpellier, France

    dguin@math.univ-montp2.fr

Mark Hovey, Wesleyan University, USA:

    mhovey@wesleyan.edu

George Janelidze, A. Razmadze Mathematical Institute, Georgia:

    gjanel@rmi.acnet.ge

Rick Jardine, University of Western Ontario, Canada:

    jardine@uwo.ca

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

R. James Milgram, Stanford University, USA:

    milgram@math.stanford.edu

Alexander Mishchenko, Moscow State University, Russia

    asmish@mech.math.msu.su

Maria Cristina Pedicchio, University of Trieste, Italy:

    pedicchi@uts.univ.trieste.it

Andrew Ranicki, University of Edinburgh, UK:

    a.ranicki@edinburgh.ac.uk

J. Nigel Ray, University of Manchester, UK:

    nige@ma.man.ac.uk

Ulf Rehmann, University of Bielefeld, Germany:

    rehmann@mathematik.uni-bielefeld.de

Jonathan M. Rosenberg, University of Maryland, USA:

    jmr@math.umd.edu

Lionel Schwartz, University of Paris 13, France:

    schwartz@math.univ-paris13.fr

James Stasheff, University of North Carolina, USA:

    jds@math.unc.edu

Ross Street, Macquarie University, Australia:

    street@macadam.mpce.mq.edu.au

Walter Tholen, York University, Canada:

    tholen@mathstat.yorku.ca

Charles A. Weibel, Rutgers University, New Brunswick, USA:

    weibel@euler.rutgers.edu

Algebraic Topological Methods in Computer Science

Proceedings of a Workshop Held at Stanford University

July 30 – August 3, 2001

Edited by Gunnar Carlsson