Subject: new Hopf listings
Date: 08 Jan 2003 07:38:32 -0500
From: Mark Hovey
Reply-To: mhovey@wesleyan.edu
To: dmd1@lehigh.edu
Date: Sat, 17 Jan 1998 18:19:15 EST
From: dmd1@lehigh.edu (DONALD M. DAVIS)
Subject: new Hopf listings
To: Distribution.List@lehigh.edu (toplist)
X-UIDL: aacd4710beaa4a6483935a131ded8f1b
Xref: picard.math.wesleyan.edu davis:291
Happy New Year! I remind you that your abstracts must contain your name
and the title of the paper at a minimum. I have had to add these in by
hand in a couple of recent cases.
7 new papers this time, from BrownR-Higgins, Jiang, Luo, Madsen-Weiss
(the proof of the Mumford conjecture!), MauerOats, McClure-SmithJH, and
Symonds.
Mark Hovey
New papers appearing on hopf between 12/01/02 and 01/08/03
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR-Higgins/cubabgp3
Title of Paper: Cubical abelian groups with connections\\ are
equivalent to chain complexes
Author(s): Ronald Brown and Philip J. Higgins
AMS Classification numbers
xxx LANL archive: math.AT/0212157
Addresses of Authors: Ronald Brown
Mathematics Division \\ School of Informatics, \\ University of
Wales, Bangor \\Gwynedd LL57 1UT, U.K.
Philip J. Higgins,
Department of Mathematical Sciences, \\ Science Laboratories, \\ South Rd., \\
Durham, DH1 3LE, U.K
Email address of Authors r.brown@bangor.ac.uk
p.j.higgins@durham.ac.uk
Abstract: The theorem of the title is deduced from the
equivalence between crossed complexes and cubical
$\omega$-groupoids with connections proved by the authors in 1981.
In fact we prove the equivalence of five categories defined
internally to an additive category with kernels.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Jiang/realization
Title of Paper: On the realization of the unstable modules
Author: JIANG Dong Hua
AMS Classification numbers: 55N99, 55S10
math.AT/0212054
Address of Author: LAGA, Institut Galilee, UMR 7539
University Paris Nord, Avenue Jean-Baptiste Clement
93430 VILLETANEUSE, FRANCE
Email address of Author: donghua.jiang@m4x.org
In this article, we give some restrictions about the structure of an
unstable module, which should be verified providing this module is the
reduced mod 2 cohomology of a space or a spectrum. We begin by studing
the structure of the sub-modules of \Sigma^s H^\ast(B(Z/2)^{\oplus d};
Z/2)^{\oplus \alpha_d} (s \geq 0, \alpha_d > 0), i.e., the unstable
modules whose nilpotent filtration has length 1. Next, we generelise
this result for the unstable modules whose nilpotent filtration has a
finite length, and who verified an additional condition. The result says
that under some hypothesis, the reduced mod 2 cohomology of a space or a
spectrum does not have arbitrary big gaps in its structure. This result
is obtained by applying the famous Adams' theorem about the Hopf
invariant and the classification of the injective unstable modules.
For the unstable modules satisfing the condition of the theorem 3 (for
example, any suspension of a sub-module of H^\ast(B(Z/2)^{\oplus d};
Z/2)^{\oplus \alpha_d}, the theorem 3 gives the upper bound of the
length of the gaps in the modules, which means the module does not
contain arbitrary big gaps. So when the module is reduced satisfing the
condition of the theorem 4, its weight should be infinite. This gives us
so many examples of the non-realizable unstable modules: F(n), any
tensor product of F(n_i), etc. (These examples can also be proved by the
theorem of Lionel Schwartz about the Kuhn conjecture, which was
generalised by F-X. Dehon - G. Gaudens.)
This article is written in french and the work is done under the
direction of L. Schwartz.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Luo/pre
Closed model categories for presheaves of simplicial groupoids and
presheaves of 2-groupoids
Zhi-ming Luo
We prove that the category of presheaves of simplicial groupoids
and the category of presheaves of 2-groupoids have Quillen closed
model structures. We also show that the homotopy categories
associated to the two categories are equivalent to the homotopy
categories of simplicial presheaves and homotopy 2-types,
respectively.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Madsen-Weiss/mumf
The stable moduli space of Riemann surfaces: Mumford's conjecture
Ib Madsen and Michael Weiss
AMS classification numbers 57R50; 14H15, 32G15, 57R45, 57M99
Submitted to arXiv: math.AT/0212321
Institute for the Mathematical Sciences
Aarhus University
8000 Aarhus C
Denmark
Department of Mathematics
University of Aberdeen
Aberdeen AB24 3UE
United Kingdom
imadsen@imf.au.dk m.weiss@maths.abdn.ac.uk
The main result of this paper amounts to a complete evaluation
of the integral cohomological structure of the stable mapping class
group (i.e, the group of isotopy classes of automorphisms
of a connected oriented surface of "large" genus).
In particular it verifies the conjecture of D.Mumford
about the rational cohomology of the stable mapping class group.
It is part of a more recent development in the field which
began with Ulrike Tillmann's result (Invent. Math., 1997) that the
plus construction makes the classifying space of the stable
mapping class group into an infinite loop space. This led to a
stable homotopy theory version of Mumford's conjecture, stronger than
the original (Madsen and Tillmann, Invent. Math., 2001).
We prove the extended version of Mumford's conjecture by a mixture
of techniques from singularity theory and from homotopy theory. The
stability theorem of J.Harer (Annals of Math., 1985) and the
"First Main theorem" of V.Vassiliev ("Complements of Discriminants
of smooth maps: Topology and Applications", Trans. of Math. Monographs Vol.98,
revised edition, Amer. Math. Soc. 1994) are prominent components
of our proof.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/MauerOats/algebraic-calc
Algebraic Goodwillie calculus and a cotriple model for the remainder
Andrew Mauer-Oats
We define an ``algebraic'' version of the Goodwillie tower, P_n^alg
F(X), that depends only on the behavior of F on coproducts of X. When F
is a functor to connected spaces or grouplike H-spaces, the functor
P_n^alg F is the base of a fibration whose fiber is the simplicial space
associated to a cotriple built from the (n+1) cross effect of the
functor F. When the connectivity of X is large enough (for example,
when F is the identity functor and X is connected), the algebraic
Goodwillie tower agrees with the ordinary (topological) Goodwillie
tower, so this theory gives a way of studying the Goodwillie
approximation to a functor F in many interesting cases.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/McClure-SmithJH/McClureSmith2_1
Multivariable cochain operations and little $n$-cubes.
James E. McClure and Jeffrey H. Smith
18D50, 55P48, 16E40
math.QA/0106024
Department of Mathematics
Purdue University
150 N. University Street
West Lafayette, IN 47907-2067
mcclure@math.purdue.edu jhs@math.purdue.edu
This is a revision of a paper first posted June 4, 2001. It will appear in the
Journal of the AMS.
In this paper we construct a small $E_\infty$ chain operad $\S$ which acts
naturally on the normalized cochains $S^*X$ of a topological space. We also
construct, for each $n$, a suboperad $\S_n$ which is quasi-isomorphic to the
normalized singular chains of the little $n$-cubes operad. The case $n=2$
leads to a substantial simplification of our earlier proof of Deligne's
Hochschild cohomology conjecture.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Symonds/morava
The Tate-Farrell cohomology of the Morava Stabilizer Group $S_{p-1}$ with coefficients in
$E_{p-1}$
Peter Symonds
We calculate the Tate-Farrell cohomology of the Morava stabilizer group $S_{p-1}$ with
coefficients in the moduli space $E_{p-1}$ for odd primes $p$.
---------------------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 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, go to
http://hopf.math.purdue.edu and use the web form. You can also use
anonymous ftp as above. First 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.