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, deleted, edited,, Mail-from: From dmd1@lehigh.edu Sat Jan 17 18:19:15 1998 Received: from nss4.cc.Lehigh.EDU (root@nss4.CC.Lehigh.EDU [128.180.1.13]) by mail.wesleyan.edu (8.8.6/8.7.3) with ESMTP id SAA10234 for ; Sat, 17 Jan 1998 18:20:52 -0500 (EST) Received: from ns4-1.CC.Lehigh.EDU (root@ns4-1.CC.Lehigh.EDU [128.180.1.42]) by nss4.cc.Lehigh.EDU (8.8.8/8.8.5) with ESMTP id SAA119110; Sat, 17 Jan 1998 18:23:02 -0500 Received: (from dmd1@localhost) by ns4-1.CC.Lehigh.EDU (8.8.5/8.8.5) id SAA39528; Sat, 17 Jan 1998 18:19:17 -0500 Message-Id: <199801172319.SAA39528@ns4-1.CC.Lehigh.EDU> Date: Sat, 17 Jan 1998 18:19:15 EST From: dmd1@lehigh.edu (DONALD M. DAVIS) X-Mailer: SENDM [Version 2.0.17] Subject: new Hopf listings To: Distribution.List@lehigh.edu (toplist) Content-Type: text X-UIDL: aacd4710beaa4a6483935a131ded8f1b Lines: 256 Xref: picard.math.wesleyan.edu davis:291 X-Gnus-Newsgroup: davis:291 Sun Jan 18 06:29:52 1998 *** EOOH *** Date: Sat, 17 Jan 1998 18:19:15 EST From: dmd1@lehigh.edu (DONALD M. DAVIS) Subject: new Hopf listings To: Distribution.List@lehigh.edu (toplist) Content-Type: text X-UIDL: aacd4710beaa4a6483935a131ded8f1b Xref: picard.math.wesleyan.edu davis:291 X-Gnus-Newsgroup: davis:291 Sun Jan 18 06:29:52 1998 8 new papers this time, including a disproof of the chromatic splitting conjecture by Shimomura and Wang. Mark Hovey New papers uploaded to hopf between 9/20/99 and 10/25/99. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Bendersky-DavisD/marspin Title: The 1-line of the K-theory Bousfield-Kan spectral sequence for Spin(2n+1) Authors: Martin Bendersky and Donald M. Davis mbenders@shiva.math.hunter.cuny.edu ddavis@math.jhu.edu Abstract: For X a simply-connected finite H-space, there is a Bousfield-Kan spectral sequence which converges to the homotopy groups of the K-completion of X. When X=Spin(2n+1), we expect that these homotopy groups equal the v1-periodic homotopy groups of X in dimension greater than n^2. In this paper, we accomplish two things: (1) We prove that, for any X, the 1-line of the spectral sequence is determined explicitly by K-theory and Adams operations. (2) For X=Spin(2n+1), we make an explicit computation of this 1-line. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/KrauseH/ARtriangle Title: Auslander-Reiten theory via Brown representability Author: Henning Krause E-mail: henning@mathematik.uni-bielefeld.de Abstract: We develop an Auslander-Reiten theory for triangulated categories which is based on Brown's representability theorem. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/McClure-SmithJH/deligne_conj A solution of Deligne's conjecture. James E. McClure and Jeffrey H. Smith mcclure@math.purdue.edu jhs@math.purdue.edu ABSTRACT: Deligne asked in 1993 whether the Hochschild cochain complex of an associative ring has a natural action by the singular chains of the little 2-cubes operad. In this paper we give an affirmative answer to this question. We also show that the topological Hochschild cohomology spectrum of an associative ring spectrum has an action of an operad equivalent to the little 2-cubes. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Menichi/Cohomology_Fiber Title: On the Cohomology algebra of a fiber Author: Luc Menichi Luc.Menichi@univ-angers.fr Abstract: Let $f:E\rightarrow B$ be a fibration of fiber $F$. Eilenberg and Moore have proved that there is a natural isomorphism of vector spaces between $H^{*}(F;\mathbb{F}_p)$ and $\mbox{Tor}^{C^{*}(B)}(C^{*}(E),\mathbb{F}_p)$. Generalizing the rational case proved by Sullivan, Anick proved that if $X$ is a finite $r$-connected CW-complex of dimension $\leq rp$ then the algebra of singular cochains $C^{*}(X;\mathbb{F}_p)$ can be replaced by a commutative differential graded algebra $A(X)$ with the same cohomology. Therefore if we suppose that $f:E\hookrightarrow B$ is an inclusion of finite $r$-connected CW-complexes of dimension $\leq rp$, we obtain an isomorphism of vector spaces between the algebra $H^{*}(F;\mathbb{F}_p)$ and $\mbox{Tor}^{A(B)}(A(E),\mathbb{F}_p)$ which has also a natural structure of algebra. Extending the rational case proved by Grivel-Thomas-Halperin, we prove that this isomorphism is in fact an isomorphism of algebras. In particular, $H^{*}(F;\mathbb{F}_p)$ is a divided powers algebra and $p^{th}$ powers vanish in the reduced cohomology $\tilde{H}^{*}(F;\mathbb{F}_p)$. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Notbohm/decomposition HOMOLOGY DECOMPOSITIONS FOR CLASSIFYING SPACES OF FINITE GROUPS ASSOCIATED TO MODULAR REPRESENTATIONS D. Notbohm For a prime $p$, a homology decomposition of the classifying space $BG$ of a finite group $G$ consists of a functor $F :\BD @>>> \spaces$ from a small category into the category of spaces and a map $\hcl{} F @>>> BG$ from the homotopy colimit to $BG$ which induces an isomorphism in mod-$p$ homology. Associated to a modular representation $G @>>> Gl(n;\fp)$ we construct a family of subgroups closed under conjugation, which gives rise to three different homology decompositions, the so called subgroup, centralizer and normalizer decomposition. For an action of $G$ on a $\fp$-vector space $V$, the collection consist of the isotropy groups of all nontrivial proper subspaces of $V$ with nontrivial $p$-Sylow subgroup. These decomposition formulas connect the modular representation theory of $G$ with the homotopy theory of $BG$. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Shimomura-Wang/L2S0 The homotopy groups $\pi_*(L_2S^0)$ at the prime 3 Katsumi Shimomura and Xiangjun Wang katsumi@math.kochi-u.ac.jp xwang@math.kochi-u.ac.jp The homotopy groups $\pi_*(L_2S^0)$ of the $L_2$-localized sphere are determined by studying the Bockstein spectral sequence. The results indicate also the homotopy groups $\pi_*(L_{K(2)}S^0)$ and we see that the fiber of the localization map $L_2S^0_3\to L_{K(2)}S^0$ is homotopic to $\Sigma^{-2}L_1S^0_3$, while Hopkins' chromatic splitting conjecture says that it has three summands. [Editor: this requires the font "min10" to print correctly. I don't have this font, so the ps, lj, and pdf files may have small imperfections] This is a slightly revised version of the one received originally Sept 1. (but not announced on this list because of font difficulties) 7. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Tsukiyama/forget8 We consider the forgetful map from the group of equivariant self equivalences to the group of non-equivariant self equivalences. A sufficient condition for this forgetful map being a monomorphism is obtained. Several examples are given. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/WarnerG/warner-book Topics in Topology and Homotopy Theory Garth Warner warner@math.washington.edu eps file "top-homotopy.eps" included This book is a systematic account of the homotopical foundations of algebraic topology. The depth of coverage is substantial and I have made a point to include material which is ordinarily not included. Here is a sample of what is taken up. (1) Nilpotency and its role in homotopy theory. (2) Bousfield's theory of the localization of spaces and spectra. (3) Homotopy limits and colimits and their applications. (4) The James construction, symmetric products, and the Dold-Thom theorem. (5) Brown and Adams representability in the setting of triangulated categories. (6) Operads and the May-Thomason theorem on the uniqueness of infinite loop space machines. (7) The plus construction and theorems A and B of Quillen. (8) Hopkins' global picture of stable homotopy theory. (9) Model categories, cofibration categories, and Waldhausen categories. (10) The Dugundji extension theorem and its consequences. ---------------------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.