Homology, Homotopy and Applications

Volume 3(2), 2001

1. Introduction Gunnar Carlsson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

2. Problem Session Gunnar Carlsson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii–xv

3. Equivariant formal group laws and complex oriented cohomology theories J.P.C. Greenlees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225–263

4. Equivariant orientation theory S.R. Costenoble, J.P. May and S. Waner . . . . . . . . . . . . . . . . . . . . . . . . . . 265–339

5. Cores of spaces, spectra, and E ring spectra P. Hu, I. Kriz and J.P. May . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341–354

6. Idempotents and Landweber exactness in brave new algebra J.P. May . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355–359

7. Stacks and the homotopy theory of simplicial sheaves J.F. Jardine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361–384

8. The Geometry of the Local Cohomology Filtration in Equivariant Bordism Dev P. Sinha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385–406

9. The tangent bundle of an almost-complex free loopspace Jack Morava . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407–415

10. Base change functors in the A1-stable homotopy category Po Hu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417–451

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. 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 adn .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 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 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 380093, Georgia.

hvedri@rmi.acnet.ge

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

Equivariant Stable Homotopy Theory and Related Areas

Proceedings of a Workshop Held at Stanford University

August 2000

Edited by Gunnar Carlsson