Subject: new Hopf listings From: Mark Hovey Date: 10 Jan 2005 14:54:10 -0500 To: dmd1@lehigh.edu 4 new papers this month, from Bendersky-Churchill, Hovey, Naumann, and Zivaljevic. Mark Hovey New papers appearing on hopf between 12/14/04 and 1/10/05 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Bendersky-Churchill/NormalForms Title: A spectral sequence approach to normal forms. Authors: Martin Bendersky & Richard C. Churchill Address: CUNY/Hunter College, Graduate Center New York, NY 10021 AMS Classification: 55T05, 34C20 Email: mbenders@math.hunter.cuny.edu rchurchi@math.hunter.cuny.edu Abstract: The theory of normal forms has been around since Poincare's time. An incomplete list of applications are to vector fields, Hamiltonians at equilibria, differential equations and singularity theory. In general one tries to modify a given element in a Lie algebra into a particularly useful form. The algorithm that performs the conversion (the normal form algorithm) can be a formidable computation. In this paper we generalize the notion of normal form to that of an initially linear group representation. In this general setting we are able to interpret the normal form algorithm as a calculation of a particularly simple spectral sequence. As a consequence we show that various vector spaces that appear in the process of carrying out the normal form algorithm are invariants of the orbit of the group representation. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey/prod-spec-seq The generalized homology of products Mark Hovey Wesleyan University mhovey@wesleyan.edu We construct a spectral sequence that computes the E-homology of a product of spectra. The E_{2}-term of this spectral sequence consists of the right derived functors of product in the category of E_{*}E-comodules, and the spectral sequence always converges (with a horizontal vanishing line at E_{infty}) when E is the Johnson-Wilson theory E(n) and each factor of the product is L_{n}-local. We are able to prove some results about the E_{2}-term of this spectral sequence; in particular, we show that the E(n)-homology of a product of E(n)-module spectra X^{\alpha} is just the comodule product of the E(n)_{*}X^{\alpha}. This spectral sequence is relevant to the chromatic splitting conjecture. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Naumann/comodlandweber Comodule categories and the geometry of the stack of formal groups N. Naumann niko.naumann@mathematik.uni-regensburg.de We generalise recent results of M. Hovey and N. Strickland on comodule categories for Landweber exact algebras using the formalism of algebraic stacks. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Zivaljevic/synergia Title: Equipartitions of measures in R4 Author: Rade Zivaljevic AMS Class.: 52A39; 52C35; 55S40; 57R22; 57R91; 68P30 arXiv:math.CO/0412483 v1 December 2004 Address: Mathematical Institute SANU, Knez Mihailova 35/1, p.o. box 367 11001 Belgrade Serbia and Montenegro e-mail: rade@turing.mi.sanu.ac.yu A measure in R4 admits an equipartition by 4 hyperplanes, provided it is symmetric with respect to a 2-dimensional, affine subspace L of R4. The computation is based on the Koschorke's exact singularity sequence for groups of normal bordisms and the remarkable properties of the essentially unique, balanced binary Gray code in dimension 4. ---------------------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 Web browser 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 should submit an abstract as well. Clarence has explicit instructions for the form of this abstract: see http://hopf.math.purdue.edu/new-html/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 at math.purdue.edu telling him what you have uploaded. The largest archive of math preprints is at http://arxiv.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 the arXiv, send e-mail to math@arxiv.org with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.