Subject: new Hopf listings Date: 13 Nov 2002 09:29:35 +0000 From: nsthov01@newton.cam.ac.uk (M.A. Hovey) Hopf received nine new papers in just nine days, so its time to announce them again already. There are papers from Anton, Broto-Levi-Oliver, Christensen-Dwyer-Isaksen, Jardine (3), and Strickland (3). Also, I just recently found out that it seems to be impossible to put files on Hopf using anonymous ftp. We are trying to fix this, but in the meantime I suggest using the web form. Mark Hovey New papers appearing on hopf between 11/04/02 and 11/13/02 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Anton/elementary.invariant Title of Paper: An elementary invariant problem and general linear group cohomology restricted to the diagonal subgroup Author: Marian F. Anton AMS Classification numbers: 57T10, 20J05, 19D06, 55R40 Address of Author: University of Sheffield, Department of Pure Mathematics, Hicks Building, Sheffield, S3 7RH, U.K. Email address of Author: Marian.Anton@imar.ro Conjecturally, for p an odd prime and R a certain ring of p-integers, the stable general linear group GL(R) and the etale model for its classifying space have isomorphic mod p cohomology rings. In particular, these two cohomology rings should have the same image with respect to the restriction map to the diagonal subgroup. We show that a strong unstable version of this last property holds for any rank if p is regular and certain homology classes for SL(2,R) vanish. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Broto-Levi-Oliver/blo-surv The theory of $p$-local groups: a survey by C. Broto, R. Levi, and B. Oliver This paper is a survey of recent results by the three authors, results which describe how the p-local fusion in a finite group G determines and is determined by the homotopy type of the p-completion of its classifying space BG. This connection then suggested to us the construction of certain spaces (classifying spaces of ``p-local finite groups'' and ``p-local compact groups'') which have many of the same properties as have p-completed classifying spaces of finite and compact Lie groups, and which can be characterized in homotopy theoretic terms. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Christensen-Dwyer-Isaksen/obstruction (This is an update) Obstruction theory in model categories J. Daniel Christensen, William G. Dwyer and Daniel C. Isaksen MSC: 55S35, 55U35, 18G55 (primary); 18G30, 55P42 (secondary) Department of Mathematics University of Western Ontario London, Ontario N6A 5B7 jdc@uwo.ca Department of Mathematics University of Notre Dame South Bend, IN 46556 dwyer.1@nd.edu Department of Mathematics University of Notre Dame South Bend, IN 46556 isaksen.1@nd.edu Keywords: obstruction theory, closed model category, simplicial set, spectrum Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists. Working in an arbitrary pointed proper model category, we classify the cofibrations that have such an obstruction theory with respect to all fibrations. Up to weak equivalence, retract, and cobase change, they are the cofibrations with weakly contractible target. Equivalently, they are the retracts of principal cofibrations. Without properness, the same classification holds for cofibrations with cofibrant source. Our results dualize to give a classification of fibrations that have an obstruction theory. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/cubical2 Abstract: "Cubical homotopy theory: a beginning", by. J.F. Jardine This paper gives a closed model structure for the category of cubical sets, suitably defined, and displays an equivalence of the associated homotopy category with the ordinary homotopy category of topological spaces, or simplicial sets. Cubical complexes appeared in the early descriptions of homology theory and combinatorial homotopy theory in the middle of the twentieth century, but development of the subject area effectively stopped as simplicial sets became the dominant combinatorial model for homotopy theory as a result of the work of Kan and later Quillen. Cubical complexes have recently resurfaced as objects of fundamental interest in Pratt's theory of higher dimensional automata in concurrency theory. Department of Mathematics University of Western Ontario London, Ontario N6A 5B7 Canada URL: http://www.math.uwo.ca/~jardine/papers/ 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/gen-shea Abstract: "Generalised sheaf cohomology theory", by. J.F. Jardine This is an expanded version of notes for a set of lectures given at the Newton Institute during a NATO ASI Workshop entitled ``Homotopy Theory of Geometric Categories'' on September 23 and 24, 2002. The paper presents some of the basic features of the homotopy theory of simplicial presheaves and the stable homotopy theory of presheaves of spectra, and then displays their use in the course of giving an outline of proof of Thomason's descent theorem for Bott periodic K-theory, in the context of equivariant stable categories for profinite groups. Department of Mathematics University of Western Ontario London, Ontario N6A 5B7 Canada URL: http://www.math.uwo.ca/~jardine/papers/ 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/int-str Abstract: "Intermediate model structures for simplicial presheaves", by J.F. Jardine This note (it is not really a finished paper) shows that any set of cofibrations containing the standard set of generating projective cofibrations determines a closed model structure on the category of simplicial presheaves on a small Grothendieck site, for which the weak equivalences are the local weak equivalences in the usual sense. A condition is given for these new model structures to be cofibrantly generated; this condition is met by Blander's local projective theory. Department of Mathematics University of Western Ontario London, Ontario N6A 5B7 Canada URL: http://www.math.uwo.ca/~jardine/papers/ 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Strickland/mcurve Multicurves and equivariant cobordism Neil Strickland 55N20,55N22,55N91,14L05 Department of Pure Mathematics University of Sheffield Sheffield S3 7RH UK Let A be a finite abelian group. We set up an algebraic framework for studying A-equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal groups. We compute the equivariant cohomology of many spaces in these terms, including projective bundles (and associated Gysin maps), Thom spaces, and infinite Grassmannians. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/Strickland/rfg Realising formal groups Neil Strickland 55N20,55N22 Department of Pure Mathematics University of Sheffield Sheffield S3 7RH UK We show that a large class of formal groups can be realised functorially by even periodic ring spectra. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/Strickland/st-csi Common subbundles and intersections of divisors Neil P. Strickland 55N20 14L05 14M15 Department of Pure Mathematics University of Sheffield Hicks Building Hounsfield Road Sheffield S3 7RH UK N.P.Strickland@sheffield.ac.uk Let V_0 and V_1 be complex vector bundles over a space X. We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that the intersection of V_0 and V_1 has dimension at least k everywhere. We study various algebraic universal examples related to this question, and show that they arise from the generalised cohomology of corresponding topological universal examples. This extends and reinterprets earlier work on degeneracy classes in ordinary cohomology or intersection theory. ---------------------Instructions----------------------------- To subscribe or unsubscribe to this list, send a message to Don Davis at dmd1@lehigh.edu with your e-mail address and name. Please make sure he is using the correct e-mail address for you. To see past issues of this mailing list, point your WWW browser to http://math.wesleyan.edu/~mhovey/archive/ If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/algtop.html which also has the other messages sent to Don's list. To get the papers listed above, point your WWW client (Netscape or Internet Explorer) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There is a web form for submitting papers to Hopf on this site as well. You can also use ftp, explained below. The largest archive of math preprints is at http://xxx.lanl.gov There is an algebraic topology section in this archive. The most useful way to browse it or submit papers to it is via the front end developed by Greg Kuperberg: http://front.math.ucdavis.edu To get the announcements of new papers in the algebraic topology section at xxx, send e-mail to math@xxx.lanl.gov with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). You can also access Hopf through ftp. Ftp to hopf.math.purdue.edu, and login as ftp. Then cd to pub. Files are organized by author name, so papers by me are in pub/Hovey. If you want to download a file using ftp, you must type binary before you type get . To put a paper of yours on the archive, cd to /pub/incoming. Transfer the dvi file using binary, by first typing binary then put You should also transfer an abstract as well. Clarence has explicit instructions for the form of this abstract: see http://hopf.math.purdue.edu/new-html/submissions.html In particular, your abstract is meant to be read by humans, so should be as readable as possible. I reserve the right to edit unreadable abstracts. You should then e-mail Clarence at wilker@math.purdue.edu telling him what you have uploaded. I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive. ------- End of forwarded message -------