Subject: new Hopf listings From: Mark Hovey Date: 15 Feb 1999 01:51:23 -0500 Four new papers and a revision this time. Mark Hovey New papers uploaded to hopf between 1/21/99 and 2/14/99: 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arone-Dwyer/symmetric Partition complexes, Tits buildings and symmetric products by G. Z. Arone and W. G. Dwyer We construct a homological approximation to the partition complex, and identify it as the Tits building. This gives a homological relationship between the symmetric group and the affine group, leads to a geometric tie between symmetric powers of spheres and the Steinberg idempotent, and allows us to use the self-duality of the Steinberg module to study layers in the Goodwillie tower of the identity functor. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Cornea/morse Title of Paper: Homotopical Dynamics II: Hopf Invariants, Smoothings and the Morse Complex. Author: Octavian Cornea AMS Classification numbers: Primary 58F09, 55Q50, 55Q25; Secondary 57R70, 58F25. Addresses of Authors: UFR de Mathematiques, Universite de Lille 1, 59655 Villeneuve d'Ascq, France Email address of Authors: cornea@gat.univ-lille1.fr Text of Abstract: The ambient framed bordism class of the connecting manifold of two consecutive critical points of a Morse-Smale function is estimated by means of a certain Hopf invariant. Applications include new examples of non-smoothable Poincare duality spaces as well as an extension of the Morse complex. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Elmendorf/CWrevised2 Title: Stabilization as a CW approximation Author: A. D. Elmendorf aelmendo@math.purdue.edu Department of Mathematics Purdue University Calumet Hammond, IN 46323 AMS classification number: 55P42 This is a revised version of a paper previously posted to the archive. The results are all the same, but the proofs have been extensively revised, in the hope of improving their comprehensibility. The previous abstract reads: This paper describes a peculiar property of the category of $S$-modules constructed by the author, Kriz, Mandell, and May: the full subcategory of suspension spectra (which are all $S$-modules) forms a precise copy of the category of topological spaces. Consequently, the ``classical'' homotopy category of $S$-modules with morphisms the actual homotopy classes of maps contains a copy of unstable homotopy theory. Stabilization and stable homotopy are then induced by CW approximation as $S$-modules. One consequence is that CW complexes whose suspension spectra are CW $S$-modules must be contractible. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Karoubi/mqta (French version), or http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Karoubi/quantum (English summary) METHODES QUANTIQUES EN TOPOLOGIE ALGEBRIQUE English summary : Quantum methods in Algebraic Topology by Max Karoubi http://www.math.jussieu.fr/~karoubi/ In this paper, we present a new version of cochains in Algebraic Topology, starting with "quantum differential forms". This version provides many examples of modules over the braid group, together with a control of the non commutativity of cup-products on the cochain level. If the quantum parameter q is equal to 1, we essentially recover the commutative differential graded algebra of de Rham-Sullivan forms on a simplicial set. For topological applications, we may take either q = 1 if we are dealing with rational coefficients or q = 0 in the general case. This construction can be generalized easily in a sheaf context. From this viewpoint, we extract a new structure of "neo-algebra". This structure is detailed in section III of the English summary (section 7 in the detailed French version). This is a special case of the notion of partial algebra introduced by I. Kriz and P. May in their book (Asterisque Nr. 233, 1995). To a simplicial set X we can associate in a functorial way a neo-algebra, which cohomology is canonically isomorphic to the usual one with coefficients in k (k might be an arbitrary commutative ring). As a differential graded algebra, this neo-algebra is related to the usual algebra of cochains C*(X) by a (zigzag) sequence of natural quasi-isomorphisms. Using in an essential way some recent results of M.-A. Mandell , http://www.lehigh.edu/~dmd1/algtop.html , one may then show that this neo-algebra (up to quasi-isomorphisms and under some mild finiteness and nilpotence conditions) determines the homotopy type of X. The proof relies on the basic fact that it may be also provided with an infty -algebra structure which is related to the classical one on C*(X) by a sequence of natural quasi-isomorphisms. On a more practical level, we give a method how to compute Steenrod operations in mod. p cohomology, as well as homotopy groups of X from the neo-algebraic data which we are describing. More details will be published soon. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Schuster-Yagita/tcbp Title: Transfers of Chern classes in BP-cohomology and Chow rings Authors: B. Schuster and N. Yagita AMS Classification numbers: 55P35, 57T25, 55R35, 57T05 Addresses: B. Schuster, FB 7 Mathematik, Bergische Universitaet Wuppertal, GAussstr. 20, D-42097 Wuppertal, Germany N. Yagita, Department of Mathematics, Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan Email: schuster@math.uni-wuppertal.de and yagita@mito.ipc.ibaraki.ac.jp Abstract: We study the $BP^*$-module structures of $BP^*(BG)$ for extraspecial $2$-groups using transfer and Chern classes. These give rise to $p$-torsion elements in the kernel of the cycle map from the Chow ring to ordinary cohomology first obtained by Totaro. ---------------------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://www.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 (Mosaic, Netscape) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to conference announcements, Purdue seminars, and other math related things on this page as well. 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/pub/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.