Subject: Hopf Date: 04 Nov 2002 08:23:19 +0000 From: nsthov01@newton.cam.ac.uk (M.A. Hovey) To: dmd1@lehigh.edu 6 new papers this time, from Goerss-Henn-Mahowald-Rezk, 2 from Kadeishvili-Saneblidze, Klein, Levi-Oliver, and Rodriguez-Scherer-Viruel. Also, I fixed a stupid error in my paper Hovey/comodule so if you downloaded that before Oct. 15, you might want to download a new copy. Mark Hovey New papers appearing on hopf between 10/07/02 and 11/04/02 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Goerss-Henn-Mahowald-Rezk/ghmr-14-10-02 Title: A resolution of the K(2)-local sphere Authors: Paul Goerss, Hans-Werner Henn, Mark Mahowald and Charles Rezk Adresses: Northwestern University, Universite Louis Pasteur, Northwestern University, University of Illinois at Urbana ABSTRACT At the prime p=3, we write the spectrum L_{K(2)}S^0 as the inverse limit of a short tower of fibrations where the fibers are (suspensions of) explicit homotopy fixed point spectra E_2^{hF} with F a finite subgroup of the Morava stabilizer group. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Kadeishvili-Saneblidze/cubmodel A cubical model for a fibration by TORNIKE KADEISHVILI AND SAMSON SANEBLIDZE In the paper the notion of truncating twisting function $\tau :X\to Q$ from a simplicial set $X$ to a cubical set $Q$ and the corresponding notion of twisted Cartesian product of these sets $X\times_{\tau }Q$ are introduced. The latter becomes a cubical set whose chain complex coincides with the standard twisted tensor product $C_*(X)\otimes_{\tau_*}C_*(Q)$. This construction together with the theory of twisted tensor products for homotopy G-algebras allows to obtain multiplicative models for fibrations. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Kadeishvili-Saneblidze/permuto The twisted Cartesian model for the double path space fibration Tornike Kadeishvili and Samson Saneblidze 55R05, 55P35, 55U05, 52B05, 05A18, 05A19 math.AT/0210224 A. Razmadze Mathematical Institute Georgian Academy of Sciences M. Aleksidze st., 1 380093 Tbilisi, Georgia kade@rmi.acnet.ge A. Razmadze Mathematical Institute Georgian Academy of Sciences M. Aleksidze st., 1 380093 Tbilisi, Georgia sane@rmi.acnet.ge The paper introduces the notion of a truncating twisting function from a cubical set to a permutahedral set and the corresponding notion of twisted Cartesian product of these sets. The latter becomes a permutocubical set that models in particular the path space fibration on a loop space. The chain complex of this twisted Cartesian product in fact is a comultiplicative twisted tensor product of cubical chains of base and permutahedral chains of fibre. This construction is formalized as a theory of twisted tensor products for Hirsch algebras. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Klein/susp-spectra Moduli of Suspension Spectra by John R. Klein Wayne State University klein@math.wsu.edu For a 1-connected spectrum E, we study the moduli space of suspension spectra which come equipped with a weak equivalence to E. We construct a spectral sequence converging to the homotopy of the moduli space in positive degrees. In the metastable range, we get a complete homotopical classification of the path components of the moduli space. Our main tool is Goodwillie's calculus of homotopy functors. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Levi-Oliver/sol Construction of 2-local finite groups of a type studied by Solomon and Benson by Ran Levi and Bob Oliver A $p$-local finite group is an algebraic structure with a classifying space which has many of the properties of $p$-completed classifying spaces of finite groups. In this paper, we construct a family of 2-local finite groups, which are exotic in the following sense: they are based on certain fusion systems over the Sylow 2-subgroup of $\Spin_7(q)$ ($q$ an odd prime power) shown by Solomon not to occur as the 2-fusion in any actual finite group. Thus, the resulting classifying spaces are not homotopy equivalent to the $2$-completed classifying space of any finite group. As predicted by Benson, these classifying spaces are also very closely related to the Dwyer-Wilkerson space $BDI(4)$. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Rodriguez-Scherer-Viruel/notsimple3 Jose L. Rodriguez, Jerome Scherer, and Antonio Viruel 55P60, 20E32, 20D45 math.AT/0210405 Universidad de Almeria, Universitat Autonoma de Barcelona, and Universidad de Malaga, Spain jlrodri@ual.es, jscherer@mat.uab.es, viruel@agt.cie.uma.es Often a localization functor (in the category of groups) sends a finite simple group to another finite simple group. We study when such a localization also induces a localization between the automorphism groups and between the universal central extensions. As a consequence we exhibit many examples of localizations of finite simple groups which are not simple. ---------------------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. 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