Subject: new Hopf listings Date: 03 Aug 2001 14:26:46 -0400 From: Mark Hovey There are 7 new papers this time. Mark Hovey New papers appearing on hopf between 7/13/01 and 8/3/01 1. http://hopf.math.purdue.edu/cgi-bin/generate?/CohenR-JonesJDS/stringhtpy Title: A homotopy theoretic realization of string topology Authors: Ralph L. Cohen and John D.S. Jones AMS Classification numbers: 55N45 57R19 18D50 Addresses: Cohen: Dept. of Mathematics, Stanford University, Stanford, CA 94305 Jones: Dept. of Mathematics, University of Warwick, Coventry CV4 7AL England Email: Cohen: ralph@math.stanford.edu Jones: jdsj@maths.warwick.ac.uk Let M be a closed, oriented manifold of dimension d. Let LM be the space of smooth loops in M. Chas and Sullivan have recently defined a kind of intersection product on the homology H_*(LM) of total degree -d. They then investigated other structure that this product induces, including a Lie algebra structure on H_*(LM), and an induced product on the S^1 equivariant homology, H_*^{S^1}(LM) . These algebraic structures, as well as others, came under the general heading of the ``String topology" of M. In this paper we describe a realization of the Chas - Sullivan loop product in terms of a ring spectrum structure on the Thom spectrum of a certain virtual bundle over the loop space. We show that this ring spectrum structure extends to an operad action of the the ``cactus operad", originally defined by Voronov, which is equivalent to the operad of framed disks in R^2. We then describe a cosimplicial model of this spectrum and, by applying the singular cochain functor to this cosimplicial spectrum we show that this ring structure can be interpreted as the cup product in the Hochschild cohomology of the cochains, HH^*(C^*(M); C^*(M)). 2. http://hopf.math.purdue.edu/cgi-bin/generate?/dosSantos-Lima_Filho/quat Title: Quaternionic algebraic cycles and reality Authors: Pedro F. dos Santos (pedfs@math.ist.utl.pt) Instituto Superior Técnico Lisboa, Portugal and Paulo Lima-Filho (plfilho@math.tamu.edu) Texas A&M university College Station, Texas USA AMS classification: 55P91; Secondary 14C05, 19L47, 55N91 Abstract In this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real Brauer-Severi varieties, under the action of the Galois group Gal(C/R). Appropriate stabilizations of these spaces yield two equivariant spectra. The first one classifies Dupont/Seymour's quaternionic K-theory, and the other one classifies and equivariant cohomology theory Z^*(-) which is a natural recipient of characteristic classes KH^*(X) --> Z^*(X) for quaternionic bundles over Real spaces X. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Hollander/Ho-Th-Stacks A Homotopy Theory for Stacks Sharon Hollander Department of Mathematics, MIT Cambridge, MA 02139 sharon@math.mit.edu AMS Classification: Primary 14A20 ; Secondary 18G55, 55U10 We give a homotopy theoretic characterization of stacks on a site $\cC$ as the {\it homotopy sheaves} of groupoids on $\cC$. We use this characterization to construct a model category in which stacks are the fibrant objects. We compare different definitions of stacks and show that they lead to Quillen equivalent model categories. In addition, we show that these model structures are Quillen equivalent to the $S^2$-nullification of Jardine's model structure on sheaves of simplicial sets on $\cC$. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Huettemann-Roendigs/twisted Title: Twisted Diagrams Authors: Thomas Huettemann and Oliver Roendigs Author addresses: Thomas Huettemann Oliver Roendigs Department of Mathematical Sciences Fakultaet fuer Mathematik King's College, University of Aberdeen Universitaet Bielefeld Aberdeen AB24 3FX Postfach 10 01 31 UK D-33501 Bielefeld Germany Email: huette@maths.abdn.ac.uk (T. Huettemann) oroendig@mathematik.uni-bielefeld.de (O. Roendigs) Abstract: Twisted diagrams are generalised diagrams: the vertices are allowed to live in different categories, and the structure maps act through specified "twisting" functors between these categories. Examples include spectra (in the sense of homotopy theory) and quasi-coherent sheaves of modules on an algebraic variety. We construct a twisted version of Kan extensions and establish various model category structures (with pointwise weak equivalences). Using these, we propose a definition of ``homotopy sheaves'' and show that a twisted diagram is a homotopy sheaf if and only if it gives rise to a ``sheaf in the homotopy category''. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/presheaves Title of paper: Presheaves of chain complexes Author: J.F. Jardine AMS Classification numbers: 55P42 55U15 18G15 Address of Author: Department of Mathematics University of Western Ontario London, Ontario N6A 5B7 Canada Email: jardine@uwo.ca This paper gives the basic constructions for homology theory in the category of modules over a presheaf of commutative rings with unit. The category of simplicial modules inherits a proper closed simplicial model structure from the category of simplicial presheaves. The corresponding stable category is described by several different models, including infinitely graded chain complexes, spectrum objects in simplicial modules, and symmetric spectrum objects in simplicial modules. The tensor product of simplicial modules induces a symmetric monoidal tensor product on the category of symmetric spectrum objects, by analogy with the construction of the smash product for symmetric spectra. This paper is in preliminary form only, and is expected to pass through several revisions. Proofs of the displayed results are in place, but it is expected that more material on Tor functors and the relation with motivic homotopy theory will be added later. The paper is available in dvi, ps and pdf formats at Jardine's home page. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Lesh/uass-so-model A conjecture on the unstable Adams spectral sequences for SO and U Kathryn Lesh Subject Classification: 55T15, 55Q52, 55U99 Department of Mathematics Union College Schenectady, NY 12308 Telephone number: (518)388-6246 klesh@member.ams.org In this paper we give a systematic account of a conjecture suggested by Mark Mahowald on the unstable Adams spectral sequences for the groups SO and U. The conjecture is related to a conjecture of Bousfield on a splitting of the E_{2}-term and to an algebraic spectral sequence constructed by Bousfield and Davis. In this paper, we construct and realize topologically a chain complex which is conjectured to contain in its differential the structure of the unstable Adams spectral sequence for SO. A filtration of this chain complex gives rise to a spectral sequence that is conjectured to be the unstable Adams spectral sequence for SO. If the conjecture is correct, then it means that the entire unstable Adams spectral sequence for SO is available from a primary level calculation. We predict the unstable Adams filtration of the homotopy elements of SO based on the conjecture, and we give an example of how the chain complex predicts the differentials of the unstable Adams spectral sequence. Our results are also applicable to the analogous situation for the group U. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Wilkerson/newring Title: Rings of invariants and inseparable forms of algebras over the Steenrod algebra Author: Clarence W. Wilkerson, Jr. Purdue University wilker@math.purdue.edu This is the final version of the paper "ringall", one of the first papers on the Hopf archive. It's due to appear in the JAMI2000 proceedings. ---------------------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 (Netscape< Internet Explorer) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to 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/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.