Subject: new Hopf listings Date: 01 Dec 2002 06:55:53 +0000 From: nsthov01@newton.cam.ac.uk (M.A. Hovey) To: dmd1@lehigh.edu Anonymous ftp is now fixed, so you can use this method to put papers on Hopf if you prefer it to the web form. Both are better than e-mail. 4 new papers this time, from McClure-SmithJH, Nam, Palmieri, and Saneblize-Umble. Mark Hovey New papers appearing on hopf between 11/13/02 and 12/01/02 1. http://hopf.math.purdue.edu/cgi-bin/generate?/McClure-SmithJH/McClure-Smith3 Cosimplicial Objects and little $n$-cubes. I. James E. McClure and Jeffrey H. Smith AMS Classification Numbers 18D50; 55P48 Submitted to arXiv: math.QA/0211368 Department of Mathematics Purdue University 150 N. University Street West Lafayette, IN 47907-2067 mcclure@math.purdue.edu jhs@math.purdue.edu In this paper we show that if a cosimplicial space or spectrum $X^\bullet$ has a certain kind of combinatorial structure (we call it a $\Xi^n$-structure) then the total space of $X^\b$ has an action of a certain operad which is weakly equivalent to the little $n$-cubes operad. The $n\leq 2$ case was proved by a more complicated argument in our earlier paper A Solution of Deligne's Hochschild Cohomology Conjecture (http://front.math.ucdavis.edu/math.QA/9910126). In the special case $n=\infty$, we define a symmetric monoidal structure $\boxtimes$ on cosimplicial spaces and show that if $X^\b$ is a commutative $\boxtimes$-monoid then the total space of $\X^\b$ is an $E_\infty$ space. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Nam/namInvent A-generateurs generiques pour l'algebre polynomiale by Tran Ngoc Nam Nous résolvons génériquement le problème ``hit'' (posé en 1986 par Franklin P. Peterson) par la découverte en degrés génériques d'un système générateur minimal explicite pour l'algèbre polynomiale comme module sur l'algèbre de Steenrod mod 2. Cette solution implique en particulier un résultat de J. Repka-P. Selick, une partie de celui de M. C. Crabb-J. R. Hubbuck et nous permet en même temps de vérifier une conjecture due à M. Kameko. Ce système générateur sera appliqué à l'étude du transfert algébrique de W. M. Singer et de la représentation modulaire du groupe linéaire général. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Palmieri/quotient Some quotient Hopf algebras of the dual Steenrod algebra by J. H. Palmieri Fix a prime p, and let A be the polynomial part of the dual Steenrod algebra. The Frobenius map on A induces the Steenrod operation P^0 on cohomology, and in this paper, we investigate this operation. We point out that if p=2, then for any element in the cohomology of A, if one applies P^0 enough times, the resulting element is nilpotent. We conjecture that the same is true at odd primes, and that "enough times" should be "once". The bulk of the paper is a study of some quotients of A in which the Frobenius is an isomorphism of order n. We show that these quotients are dual to group algebras, the resulting groups are torsion-free, and hence every element in Ext over these quotients is nilpotent. We also try to relate these results to the questions about P^0. The dual complete Steenrod algebra makes an appearance. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Saneblidze-Umble/PMAfnl Title: Diagonals on the Permutahedra, Multiplihedra and Associahedra Authors: Samson Saneblidze, Ronald Umble MSC: 55P35, 55U05 ArXive: math.AT/0209109 Abstract: We construct an explicit diagonal on the permutahedra {P_n}. Related diagonals on the multiplihedra {J_n} and the associahedra {K_n} are induced by Tonks' projection P_n --> K_{n+1} and its factorization through J_n. We use the diagonal on {K_n} to define the tensor product of A_infty-(co)algebras. We introduce the notion of a permutahedral set Z, observe that the double cobar construction Omega^{2}C_*(X) is a naturally occurring example and lift the diagonal on {P_n} to a diagonal on Z. ---------------------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 WWW client (Netscape or Internet Explorer) 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 can also use ftp, explained below. 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/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@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.