Date: Sat, 26 Sep 1998 05:39:48 -0400
From: Mark Hovey <hovey@picard.math.wesleyan.edu>
Subject: new Hopf listings

We have 9 new papers this time.

Mark Hovey

New papers uploaded to hopf between 8/19/98 and 9/26/98:

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem/amsbetti

Buildings, Group extensions and the Cohomology of Congruence Subgroups

A.Adem (U.Wisconsin)

We use methods from group cohomology and buildings to estimate
betti numbers for congruence subgroups in SL_3(Z) and Sp_4(Z).

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem-Karagueuzian/cmhess

Essential Cohomology of Finite Groups

A.Adem & D.Karagueuzian (U.Wisconsin)

Abstract:
We prove that a finite group G has Cohen--Macaulay, undetectable
mod p cohomology if and only if G is a p-group such that all its elements
of order p are central.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem-Karagueuzian-Milgram-Umla
nd/newly8

The Cohomology of the Lyons Group and Double
Covers of the Alternating Groups

A.Adem (U.Wisconsin), D.Karagueuzian (U.Wisconsin),
R.J. Milgram (Stanford U.), K. Umland (U. New Mexico).

--We compute the mod 2 cohomology of Lyons' sporadic simple group
as well as that of the double covers of A_8, S_8 and A_10.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem-Karagueuzian-Minac/fire2

On the Cohomology of Galois Groups Determined by Witt Rings

A.Adem (U.Wisconsin), D. Karagueuzian (U.Wisconsin),
J.Minac (U.Western Ontario)

Let F denote a field of characteristic different from two.  In this
paper we describe the mod 2 cohomology of a Galois group G_F (called the
W-group of F) which is known to essentially characterize the Witt ring
WF of anisotropic quadratic modules over F.  We show that its mod 2
cohomology contains the mod 2 Galois cohomology of F and that its
structure will reflect important properties of the field.  We construct
a space X_F endowed with an action of an elementary abelian group E such
that the computation of the cohomology of G_F reduces to calculating the
E-equivariant cohomology of the space.  For the case of a field which is
not formally real this amounts to computing the cohomology of an
explicit Euclidean space form, an object which is interesting in its own
right. We provide a number of examples and a substantial combinatorial
computation for the cohomology of the universal W-groups.

5.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem-Yalcin/gpext4

On Some Examples of Group Actions and Group Extensions

A.Adem (U.Wisconsin) and E.Yalcin (Indiana U.)

--We consider the problem of which 2-groups can acts freely on a
product of equidimensional spheres and show that it relates to
questions about group extensions. We apply some rather unexpected
examples from group theory to do this.

6.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Neusel/athom

The Inverse Invariant Theory Problem and Steenrod Operations

Mara D Neusel

AMS Classification: 55S10 Steenrod Algebra, 13A50 Invariant Theory, 55XX Algebra
ic Topology

AG Invariantentheorie
mdn@sunrise.uni-math.gwdg.de

This is a pure postscript file.

This is a (heavily) revised version of the paper with the same
titel put on Hopf in June. I have corrected some blunders
and at least 1001 typos, added more examples and
rewritten big parts of the story. I hope it is now more readable.

Here the original abstract once more:

This paper is devoted to the study of inverse invariant theory and its
relationship with the $\steenrod$--invariant prime spectrum of an
unstable algebra over the Steenrod algebra.  We will show that this
spectrum is a chain saturated poset.  Moreover we will prove the
existence of Thom classes, detect a fractal of the Dickson algebra in
any unstable algebra and give a counterexample to the Reverse
Landweber--Stong Conjecture.  Along the way to these results we will
generalize the famous Adams--Wilkerson theorems to arbitrary Galois
fields, have a closer look at fields and their extensions over the
Steenrod algebra, and generalize some results about the unstable part of
a module over the Steenrod algebra.

7.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Pakianathan/exponent

Title: Exponents and the Cohomology of Finite Groups.
Author: Jonathan Pakianathan
AMS Classification: Primary 20J06, 17B50, 17B56
Address of Author: Department of Mathematics, University of Wisconsin,
Madison, WI 53706.
Email: pakianat@math.wisc.edu
Status: Reprint. To appear in "The Proceedings of the A.M.S.".

This paper provides an example of a p-group G which has elements of
order p^3 in some of its integral cohomology groups but which also has
the property that p^2 annihilates H^i(G;Z) for all sufficiently high
i. This provides a counterexample to a conjecture of A. Adem which
stated that if a finite group K has an element of order p^n in one of
its integral cohomology groups then it has such an element in infinitely
many of its cohomology groups.

8.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Scheerer-DStanley/don

Title:``On the rational LS-category of a cartesian product of maps''

Authors: Hans Scheerer and Don Stanley

AMS-classification number: 55P50

Address:
Hans Scheerer
Freie Universitaet Berlin
Institut fur Mathematik II
Arnimallee 3
14195 Berlin
Germany

Don Stanley
Freie Universitaet Berlin
Institut fur Mathematik II
Arnimallee 3
14195 Berlin
Germany

email: scheerer@math.fu-berlin.de stanley@math.fu-berlin.de

Abstract:
We give an example of a rational map, $f$, such that
$cat f=cat f\times id_{S^3}=2.

9.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/DStanley/ls4

Title:``On the Lusternik-Schnirelmann category of maps''

Author: Don Stanley

AMS-classification number: 55P50

Address:
Don Stanley
Freie Universitaet Berlin
Institut fur Mathematik II
Arnimallee 3
14195 Berlin
Germany

email: stanley@math.fu-berlin.de

Abstract:
We give conditions when $cat(f \times g)<cat(f)+cat(g)$. We apply
our result to show that under suitable conditions for rational maps
$f$, $mcat(f)<cat(f)$ is equivalent to $cat(f)=cat(f\times id_{S^n})$.
Many examples with $mcat(f)<cat(f)$ satisfying our conditions are
constructed. We also resolve one open case of Ganea's conjecture
by constructing a space $X$ such that $cat(X \times S^1)=cat(X)=2$.
In fact for every $Y$, $cat(X \times Y) \leq cat(Y)+1 <cat(Y)+cat(X)$.
We show that this same $X$ has the property
$cat(X)=cat(X \times X)=cl(X \times X)=2$.

---------------------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 <RET>

before you type
get <file-name> <RET>.

To put a paper of yours on the archive, cd to /pub/incoming. Transfer
the dvi file using binary, by first typing
binary <RET>

then

put <file-name> <RET>

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.