Subject: new Hopf listings From: Mark Hovey Date: 18 Aug 1998 07:26:40 -0400 There are three new papers on Hopf this time. I have decided that I do not want to compete with xxx's excellent announcement service. I will therefore remind you how to subscribe to xxx now and, permanently, in the instructions at the end, but will no longer announce new preprints on xxx. To subscribe to xxx, send e-mail to math@xxx.lanl.gov, with subject "subscribe" (not in quotes). The body of the message should consist of the line "add AT" (without quotes). You will then be subscribed to the Algebraic Topology announcement service. A similar message works for other categories on xxx--e.g. "add GT" will give you geometric topology. Mark Hovey New papers uploaded to hopf between 7/17/98 and 8/19/98: 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Goerss/hopfring Title: Hopf rings, Dieudonn\'e modules, and $E_\ast \Omega^2S^3$. Author: Paul Goerss AMS Classification Nos: 55205, 55N20, 57T05, 16W30 Department of Mathematics Northwestern University Evanston IL 60208 pgoerss@math.washington.edu (until 8/24/98) pogerss@math.nwu.edu Abstract: Hopf algebras over the prime field with $p$ elements is an abelian category which is equivalent, by work of Schoeller, to a category of graded modules, known as Dieudonn\'e modules. Graded ring objects in Hopf algebras are called Hopf rings, and they arise in the study of unstable cohomology operations for extraordinary cohomology theories. The central point of this paper is that Hopf rings can be studied by looking at the associated ring object in Dieudonn\'e modules. They can also be computed there, and because of the relationship between Brown-Gitler spectra and Dieudonn\'e modules, calculating the Hopf ring for a homology theory $E_\ast$ comes down to computing $E_\ast\Omega^2S^3$ -- which Ravenel has done for $E = BP$. The are two major algebraic difficulties encountered in this approach. The first is to decide what a ring object is in the category of Dieudonn\'e modules, as there is no obvious symmetric monoidal pairing associated to a tensor product of modules. The second is to show that Hopf rings pass to rings in Dieudonn\'e modules. This involves studying universal examples, and here we pick up an idea suggested by Bousfield: torsion-free Hopf algebras over the $p$-adic integers with some additional structure, such as a self-Hopf-algebra map that reduces to the Frobenius, can be easily classified. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Hopkins-Mahowald/eo2homotopy title: From elliptic curves to homotopy theory authors: Mike Hopkins Mark Mahowald Department of Mathematics Department of Mathematics MIT Northwestern University Cambridge MA 02139 Evanston IL 60208 AMS class: 55P42,55P60,55N20,55N22,55Q45 Addresses: Department of Mathematics Department of Mathematics MIT Northwestern University Cambridge MA 02139 Evanston IL 60208 Email: mjh@@math.mit.edu} mahowald@math.nwu.edu Include: eo2homotopy.eps Abstract: A surprising connection between elliptic curves over finite fields and homotopy theory has been discovered by Hopkins. In this note we will follow this development for the prime 2 and discuss the homotopy which developed from this. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Sinha/mugcomps Computations in Complex Equivariant Bordism Theory by Dev Sinha Mathematics Department Box 1917 Brown University Providence, RI 02912 E-mail: dps@math.brown.edu In this paper we present computations of the ring structure of the coefficients of equivariant bordism, answering questions which have been open since these theories were first defined by Conner and Floyd and tom Dieck. We have a result which establishes an algebraic framework in which to understand equivariant bordism for any group such that any proper subgroup is contained in a proper normal subgroup. This class of groups includes abelian groups and $p$-groups. Our general result is computationally satisfying when one can find a suitable representation of $MU^G_*$. For abelian groups the map to completion at the augmentation ideal seems to be such a representation, so we make explicit computations of that map. We give applications to the geometry of lens spaces and $S^1$ actions on stably complex four-manifolds. **This paper is a revised version of a previous submission. The biggest **change is the explicit naming of ring generators of $MU^G_*$. ---------------------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.cs.wesleyan.edu/Math/Guests/Mark If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/public/www-data/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.