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.
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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.