Subject: new Hopf listings From: Mark Hovey Date: 19 Aug 1999 07:27:23 -0400 I have decided that the addresses of the authors and the Math Subject Classifications, while certainly useful in the archive itself, just get in the way in these mailings. So I have deleted them from these abstracts. Let me know if you think this is the wrong thing to do. 8 new papers this time. Mark Hovey New papers uploaded to hopf between 7/16/99 and 8/19/99. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arkowitz-Stanley/gan8 Title:"The cone length of a product of co-H-spaces and a problem of Ganea" Authors: Martin Arkowitz and Donald Stanley Abstract: It is proved that the cone length or strong category of a product of two co-H-spaces is less than or equal to two. This yields the following positive solution to a problem of Ganea. Let $\alpha \in \pi_{2p}(S^3)$ be an element of order p, p a prime $\geq 3$, and let $X(p)=S^3\cup_{\alpha}e^{2p+1}$. Then $X(p)\times X(p)$ is the mapping cone of some map $\phi:Y \rightarrow Z$, where $Z$ is a suspension. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Devinatz-Hopkins/homotopy-fixe d-point (Note: you need the file approx.ps as well as the dvi file to print this). Title: Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups Author: Ethan S. Devinatz and Michael J. Hopkins Text of Abstract: Let G be a closed subgroup of the semi-direct product of the nth Morava stabilizer group with the Galois group of the field extension of degree n of the field of p elements. We construct a "homotopy fixed point spectrum" whose homotopy fixed point spectral sequence involves the continuous cohomology of G. These spectra have the expected functorial properties and agree with the Hopkins-Miller fixed-point spectra when G is finite. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Hovey/stable-model Stabilization of Model Categories by Mark Hovey This is an update of a previous paper on the archive. Recall that the idea of this paper is to construct spectra and symmetric spectra starting from an arbitrary model category. There was a mistake in the previous version; I asserted that, whenever symmetric spectra and spectra could both be defined, they were the same up to a chain of Quillen equivalences. There is a simple argument showing that this must be false without some hypothesis. This mistake has now been fixed and the correct hypothesis added. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Hovey-Palmieri/galois Galois theory of thick subcategories in modular representation theory by Mark Hovey and John Palmieri Suppose B is a finite-dimensional cocommutative Hopf algebra over a field k. Define a thick subcategory to be a full subcategory of the category of finite-dimensional B-modules that is closed under summands and, if two out of three modules in a short exact sequence are in it, so is the third. Define a thick subcategory to be tensor-closed if it is closed under tensoring with any finite-dimensional module. The classification of these tensor-closed thick subcategories, analogous to the Hopkins-Smith classification of thick subcategories in the stable homotopy category, has been carried out for B=k[G], where G is a finite group and k is an algebraically closed field of positive characteristic, by Benson-Carlson-Rickard. A similar classification has been obtained by the current authors when B is a finite subalgebra of the mod 2 Steenrod algebra, with scalars extended to the algebraic closure of Z/2. In the present paper, we eliminate the annoying requirement that the field be algebraically closed. We show that, if the expected classification of tensor-closed thick subcategories holds for B tensor L, where L is a normal extension field of k, then it holds for B as well. The proof involves importing the basic ideas of Galois theory into axiomatic stable homotopy theory. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Joyal-Tierney/JT-chap-01 Title: An Introduction to Simplicial Homotopy Theory Authors: Andre Joyal and Myles Tierney Abstract: This is a preliminary version of the first chapter of a book on simplicial homotopy theory. It introduces simplicial sets, and supplies the basic background material, anodyne extensions, fibrations, homotopy between maps, etc, leading to a new, combinatorial proof of the existence of the classical Quillen model structure. It finishes with Milnor's Theorem showing that the category of Kan complexes and homotopy classes of maps is equivalent to the category of CW-complexes and homotopy classes of maps. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Leary/ijltork Title: A torsion projective class for a group algebra Author: Ian J. Leary Abstract: For a certain cyclic-by-finite group, we construct an element of order two in the algebraic $K_0$ of the rational group ring, whose image in $K_0$ of the complex group ring is zero. Non-triviality of the element is established using topological methods. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Leary-Nucinkis/ijlbeanCW Title: Every CW-complex is a classifying space for proper bundles Authors: Ian J. Leary and Brita E. A. Nucinkis Abstract: We prove that, up to homotopy equivalence, every connected CW-complex is the quotient of a contractible complex by an action of a discrete group, and that every CW-complex is the quotient of an aspherical complex by an action of a group of order two. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Snaith/vpsnaithBP Title: Hurewicz images in BP and related homology theories Author: Victor Snaith In this paper $BP$-theory is used to give a proof that there exists a stable homotopy element in $\pi_{2^{n+1} - 2}^{S}( {\bf R}P^{\infty})$ with non-zero Hurewicz image in $ju$-theory if and only if there exists an element of $\pi_{2^{n+1} - 2}^{S}( S^{0})$ which is represented by a framed manifold of Arf invariant one. ---------------------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.