Subject: new Hopf listings Date: 02 Sep 2001 09:42:30 -0400 From: Mark Hovey To: dmd1@lehigh.edu There are 5 new papers on Hopf this month. Mark Hovey New papers appearing on hopf between 8/3/01 and 9/2/01 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Bartels-Farrell-Jones-Reich/oneiso On the Isomorphism Conjecture in algebraic K-theory Arthur Bartels, Tom Farrell, Lowell Jones and Holger Reich The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RG, where G is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed Riemannian manifolds with strictly negative sectional curvature and an arbitrary coefficient ring R. If R is regular this leads to a concrete calculation of low dimensional K-theory groups of RG in terms of the K-theory of R and the homology of the group. AMS Classification: 19A31, 19B28, 19D35, 19D50 AT/0108139 Westfaelische Wilhelms-Universitaet, SFB 478, 48149 Muenster, Germany Department of Mathematics, SUNY, Binghamton, NY 13902, USA Department of Mathematics, SUNY, Stony Brook, NY 11794, USA Westfaelische Wilhelms-Universitaet, SFB 478, 48149 Muenster, Germany bartelsa@math.uni-muenster.de farrell@math.binghamton.edu lejones@math.sunysb.edu reichh@math.uni-muenster.de 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Berger-Fresse/CochainModel Tittle: Combinatorial operad actions on cochains Authors: Clemens Berger and Benoit Fresse Abstract: A classical E-infinity operad is formed by the bar constructions associated to the symmetric groups. Such an operad is introduced by M. Barratt and P. Eccles in the context of simplicial sets in order to have an analogue of the Milnor FK-construction for infinite loop-spaces. The purpose of the article is to prove that the associative algebra structure on the normalized cochain complex of a simplicial set extends to the structure of an algebra over the Barratt-Eccles operad. We prove also that the differential graded algebras over the Barratt-Eccles operad form a closed model category. We have similar results for the normalized Hochschild cochain complex associated to an associative algebra. More precisely, the Hochschild cochain complex is acted on by a sub-operad of the Barratt-Eccles operad which is equivalent to the classical little square operad. Mail address: Laboratoire J.A. Dieudonn\'e, Universit\'e de Nice, Parc Valrose, F-06108 Nice Cedex 02 (France). E-mail address: Clemens Berger Benoit Fresse 3. http://hopf.math.purdue.edu/cgi-bin/generate?/IsaksenD/strict Title: Strict Model Structures for Pro-Categories Author: Daniel C. Isaksen AMS Classification: 18G55, 55U35 Address: Department of Mathematics\\University of Notre Dame\\Notre Dame, IN 46556 e-mail: isaksen.1@nd.edu Abstract: We show that if C is a proper model category, then the pro-category pro-C has a strict model structure in which the weak equivalences are the levelwise weak equivalences. This is related to a major result of Edwards and Hastings. The strict model structure is the starting point for many homotopy theories of pro-objects. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Rudyak/PLstructures Piecewise linear structures on topological manifolds Yuli B. Rudyak MSC 57Q25 Submitted to xxx LANL archive: math.AT/0105047 Mathematisches Institut Universitaet Heidelberg, Im Neuenheimer Feld 288, 69120 Heidelberg, Germany \email: rudyak@mathi.uni-heidelberg.de This is a survey paper where we expose the Kirby--Siebenmann results on classification of PL structures on topological manifolds and, in particular, the homotopy equivalence TOP/PL=K(\ZZ/2.3) and the Hauptvermutung for manifolds. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Schwede-Shipley/class.final Title: Classification of stable model categories Authors: Stefan Schwede Fakultat fur Mathematik Universitat Bielefeld 33615 Bielefeld, Germany schwede@mathematik.uni-bielefeld.de and Brooke Shipley Department of Mathematics Purdue University W. Lafayette, IN, USA 47907 bshipley@math.purdue.edu AMS Classification numbers: 55U35, 55P42 Abstract: A stable model category is a setting for homotopy theory where the suspension functor is invertible. The prototypical examples are the category of spectra in the sense of stable homotopy theory and the category of unbounded chain complexes of modules over a ring. In this paper we develop methods for deciding when two stable model categories represent `the same homotopy theory'. We show that stable model categories with a single compact generator are equivalent to modules over a ring spectrum. More generally stable model categories with a set of generators are characterized as modules over a `ring spectrum with several objects', i.e., as spectrum valued diagram categories. We also prove a Morita theorem which shows how equivalences between module categories over ring spectra can be realized by smashing with a pair of bimodules. Finally, we characterize stable model categories which represent the derived category of a ring. This is a slight generalization of Rickard's work on derived equivalent rings. We also include a proof of the model category equivalence of modules over the Eilenberg-Mac Lane spectrum HR and (unbounded) chain complexes of R-modules for a ring R. Remark: Our use of lamsarrows may make the .dvi file less portable than the .ps or .pdf files. ---------------------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.