BABYL OPTIONS: -*- rmail -*- Version: 5 Labels: Note: This is the header of an rmail file. Note: If you are seeing it in rmail, Note: it means the file has no messages in it.  1, edited, forwarded,, Mail-from: From hovey@math.mit.edu Fri Feb 3 09:53:22 1995 Return-Path: Received: from nevanlinna.mit.edu by math.mit.edu (4.1/Math-2.0) id AA23567; Fri, 3 Feb 95 09:51:15 EST From: Mark Hovey Received: by nevanlinna.mit.edu; Fri, 3 Feb 95 09:51:11 EST Date: Fri, 3 Feb 95 09:51:11 EST Message-Id: <9502031451.AA21474@nevanlinna.mit.edu> To: hovey@math.mit.edu Subject: Hopf mailing list Reply-To: hovey@math.mit.edu *** EOOH *** Return-Path: From: Mark Hovey Date: July 11, 1995 09:51:11 EST To: hovey@math.mit.edu Subject: Hopf mailing list Reply-To: hovey@math.mit.edu This is the eighth installment of a mailing list of algebraic topology papers recently uploaded to Clarence Wilkerson's archive. This list is maintained by Mark Hovey (hovey@math.mit.edu). Instructions at the end. Perhaps I should mention that generally I find out about new papers on hopf the day or day after Clarence makes them available. The erratic schedule of this list is due to variability in when people put new papers on the archive. New business: 1. I have decided to distribute this list through Don Davis' topology mailing list. The effect of this on you should be minimal, except that you will receive the other submissions to Don's list as well as my mailings. This means that you should subscribe and unsubscribe through Don, not me. The instructions at the end are suitably revised to reflect this. Let me know your reactions to this, if any. 2. I now have a home page on the world-wide web!!! It contains the back issues of these mailings, and my own papers, as well as some various computer and Emacs-related links. No graphics though. The URL is http://www.mit.edu:8001/afs/athena.mit.edu/user/h/o/hovey/Public/homepage.html Add it to your bookmarks so you don't have to type it more than once! Mark Hovey Papers uploaded to Hopf between May 13 and July 10, 1995: 1. /pub/DJGreen/m24.abstract Author: David J Green Title : The 3-local cohomology of the Mathieu group M_24 Status: To appear in Glasgow Math. J. Date : Submitted 8th August 1994. Resubmitted 11th November 1994. Abstract: The localisation at the prime 3 of the integral cohomology ring of the Mathieu group $M_{24}$ is calculated. The Chern classes of the Todd representation in $GL_{11} (F_2)$ generate the even-degree part of this ring. The mod-3 cohomology ring is also calculated. [These results have been used by C. B. Thomas to prove that the elliptic cohomology of the classifying space $BM_{24}$ is generated by Chern classes, and is therefore concentrated in even dimensions.] 1991 Mathematics Subject Classification: 20J06 (primary), 20D08 2. /pub/DJGreen/p5.abstract Author: David J Green Title : Chern classes and extraspecial groups of order $p^5$ Date : 7th June 1995 A presentation is obtained for the Chern subring modulo nilradical of both extraspecial $p$-groups of order $p^5$, for $p$ an odd prime. Moreover, it is proved that, for every extraspecial $p$-group of exponent $p$, the top Chern classes of the irreducible representations do not generate the Chern subring modulo nilradical. Finally, a related question about symplectic invariants is discussed, and solved for $Sp_4 (F_p)$. The main innovation in this work is to consider extraspecial groups as central products, and to partition the maximal elementary abelian subgroups of the central product into those which lift to abelian subgroups of the corresponding direct product, and those which do not. 1991 Mathematics Subject Classification: 20J06 3. /pub/Henderson/Ext_Mon_HA.abstract (I think this is an updated version of a paper that was already on the archive-- Mark) Hopf Algebra Extensions of Monogenic Hopf Algebras Gregory D. Henderson Pennsylvania State University William M. Singer has described a cohomology theory of connected Hopf algebras which classifies extensions of a cocommutative Hopf algebra by a commutative Hopf algebra in much the same way as the cohomology of groups classifies extensions of a group by an abelian group. We compute these cohomology groups for monogenic Hopf algebras, construct an action of the base ring on the cohomology groups in the case of trivial matched pairs, and use these results to further study Singer's cohomology. 4. /pub/Thomason/thomason_SymMon_equals_Spectra.abstract Symmetric monoidal categories model all connective spectra R. W. Thomason The classical infinite loopspace machines in fact induce an equivalence of categories between a localization of the category of symmetric monoidal categories and the stable homotopy category of -1-connective spectra. 5. /pub/Welker-Ziegler-Zivaljevic/compare.abstract Abstract : Comparison Lemmas and Applications for Diagrams of Spaces V. Welker, G.M. Ziegler, R.Zivaljevic We provide a ``toolkit'' of basic lemmas for the comparison of homotopy types of (homotopy) limits of diagrams of spaces over finite partially ordered sets, among them several new ones. In the setting of this paper, we obtain simple inductive proofs that provide explicit homotopy equivalences. (In an appendix we provide the link to the general setting of diagrams of spaces over an arbitrary small category.) We show how this toolkit of old and new diagram lemmas can be used on quite different fields of applications. In this paper we demonstrate this with respect to * the ``generalized homotopy-complementation formula'' by Bj\"orner * the topology of toric varieties (which turn out to be homeomorphic to homotopy limits, and for which the homotopy limit construction provides a suitable spectral sequence), * in the study of homotopy types of arrangements of subspaces, where we establish a new, general combinatorial formula for the homotopy types of ``Grassmannian'' arrangements, and * in the analysis of homotopy types of subgroup complexes. 6. /pub/Wolbert/current.abstract Toward an algebraic classification of module spectra by J. Wolbert Department of Mathematics, University of Chicago, Chicago, IL 60637, USA Abstract: The category of modules over an $S$-algebra (\Ai\ or \Ei\ ring spectrum) has many of the good properties of the category of spectra. When the homotopy groups of the $S$-algebra in question form a sufficiently nice ring, it is possible to see the deviation of the category of modules over an $S$-algebra from the corresponding algebraic module category. In particular, many algebraic modules are realized as homotopy groups of topological modules over $S$-algebras. Examples studied include real and complex $K$-theory, both connective and periodic. Further, Bousfield localization by a smashing spectrum is shown to yield a category of modules over the localized sphere. For periodic $K$-theory, these methods yield an algebraic criterion to determine when a local spectrum is a module over the $K$-theory $S$-algebra, real or complex. ---------------------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 get the papers listed above, point your WWW client (Mosaic, Netscape) to http://hopf.math.purdue.edu/pub/hopf.html. There are links to conference announcements, Purdue seminars, and other math related things on this page as well. You can also use 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. To do this take the TeX file and save the abstract to a different file, without any \begin{document} commands or anything, and transfer that file. You can use ascii instead of binary for this. I am solely responsible for this mailing list---don't send complaints about it to Clarence. Thanks to Clarence for creating and maintaining the archive.