Subject: new Hopf listings
From: Mark Hovey
Date: 07 Nov 1998 04:58:45 -0500
Seven new papers this time. I made a typo last time: it was
Pengelley-Williams, not Pengelley-Wiliams.
Mark Hovey
New papers uploaded to hopf between 10/26/98 and 11/7/98:
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arkowitz-Scheerer/Beralgebra
(No title or author list in this abstract)
Let the space X be a 1-connected cogroup. If R is a ring,
then a cohomology (flat) product H^{p+1}(X;R) X H^{q+1}(X;R)
--->H^{p+q+1}(X;R) was defined by Arkowitz. If we set
A^p(X;R)=H^{p+1}(X;R) for p>0 and A^0(X;R)=R,then A*(X;R)
is a graded algebra. Berstein has defined a coalgebra
B_*(X;K) and dual algebra B*(X;K) when X is a cogroup
and K is a field. Our main result is that A*(X;K) and
B*(X;K) are isomorphic algebras if X has finite type over K.
It follows that the conilpotency class of X is bounded below
by the length of the longest product in the algebras B*(X;K).
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Christensen-Hovey/all-or-nothi
ng
Phantom maps and chromatic phantom maps
J. Daniel Christensen and Mark Hovey
jdc@math.jhu.edu and hovey@member.ams.org
Keywords: Phantom map, chromatic phantom map, n-phantom map,
cohomotopy, stable homotopy, spectrum, n-finite type.
Abstract:
In the first part, we determine conditions on spectra X and Y under
which either every map from X to Y is phantom, or no nonzero maps are.
We also address the question of whether such all or nothing behaviour
is preserved when X is replaced with V smash X for V finite. In the
second part, we introduce chromatic phantom maps. A map is n-phantom
if it is null when restricted to finite spectra of type at least n.
We define divisibility and finite type conditions which are suitable
for studying n-phantom maps. We show that the duality functor W_{n-1}
defined by Mahowald and Rezk is the analog of Brown-Comenetz duality
for chromatic phantom maps, and give conditions under which the
natural map Y --> W_{n-1}^2 Y is an isomorphism.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Neusel/wyoming
TITEL: Localizations over the Steenrod Algebra. The lost Chapter
AUTHOR: Mara D. Neusel
EMAIL: mdn@sunrise.uni-math.gwdg.de
mneusel@cfgauss.uni-math.gwdg.de
neusel@math.umn.edu
maramara@steenrod.mast.queensu.ca
AMS CODE: 55S10 Steenrod Algebra, 13BXX Ring Extensions and Related Topics,
55XX Algebraic Topology, 13XX Commutative Rings and Algebras
KEY WORDS: Steenrod Algebra, Unstable Algebras over the Steenrod Algebras,
Unstable Part, Localizations, Noetherianess, Integral Closure,
Dickson Algebra
ABSTRACT:
Let H be an unstable algebra over the Steenrod algebra, and let
S\subset \H be a multiplicatively closed subset. The localization
at S, i.e. S^{-1}H, inherits an action of the Steenrod algebra
from H, which is, however, in general no longer unstable. In this note
we consider the following three statements.
(1) H is Noetherian,
(2) the integral closure, \overline{H_{S^{-1}H}},
of H in the localization with respect to S
is Noetherian,
(3) \overline{H_{S^{-1}H}}= Un(S^{-1}H).
where Un(-) denotes the unstable part.
If the set S contains only (nonzero) non zero divisors and the algebras
are reduced then
(1) is equivalent to (2).
If S contains zero divisors, then only (1) \Rightarrow (2)
remains true, to show the converse is false we construct a counter
example.
The implication (2) \Rightarrow (3) is always true, while
its converse (3) \Rightarrow (2) needs a weird bunch of technical
assumptions to remain true. However, none of them can be removed:
we illustrate this also with examples.
Finally, as a technical tool, we characterize
Delta-finite algebras.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Rezk/rezk-ho-models
"A model for the homotopy theory of homotopy theory"
Charles Rezk
(Primary 55U35; Secondary 18G30)
Department of Mathematics
Northwestern University
Evanston, IL 60208
rezk@math.nwu.edu
November 3, 1998
We describe a category, the objects of which may be viewed as models
for homotopy theories. We show that for such models, ``functors
between two homotopy theories form a homotopy theory'', or more
precisely that the category of such models has a well-behaved internal
hom-object.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Rezk/rezk-sharp-maps
"Fibrations and homotopy colimits of simplicial sheaves"
Charles Rezk
(Primary 18G30; Secondary 18B25, 55R99)
Department of Mathematics
Northwestern University
Evanston, IL 60208
rezk@math.nwu.edu
November 3, 1998
We show that homotopy pullbacks of sheaves of simplicial sets over a
Grothendieck topology distribute over homotopy colimits; this
generalizes a result of Puppe about topological spaces. In addition,
we show that inverse image functors between categories of simplicial
sheaves preserve homotopy pullback squares. The method we use
introduces the notion of a sharp map, which is analogous to the notion
of a quasi-fibration of spaces, and seems to be of independent
interest.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Rodriguez-Scevenels/homology
TITLE: "Homology equivalences inducing an epimorphism on
the fundamental group"
AUTHORS:
Jose L. Rodriguez
Universitat Autonoma de Barcelona
E--08193 Bellaterra, Spain
jlrodri@mat.uab.es
http://mat.uab.es/jlrodri
Dirk Scevenels
Departement Wiskunde, Katholieke Universiteit Leuven,
Celestijnenlaan 200 B,
B--3001 Heverlee, Belgium
dirk.scevenels@wis.kuleuven.ac.be
ABSTRACT:
Quillen's plus construction is a topological construction
that kills the maximal perfect subgroup of the fundamental
group of a space without changing the integral homology
of the space. In this paper we show that there is a
topological construction that, while leaving the integral
homology of a space unaltered, kills even the intersection
of the transfinite lower central series of its fundamental
group. Moreover, we show that this is the maximal subgroup
that can be factored out of the fundamental group without
changing the integral homology of a space.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Strom/EPhant
Essential Category Weight and Phantom Maps
Jeffrey A. Strom
Wayne State University
strom@math.wayne.edu
This purpose of this paper is to study the relationship
between maps with infinite essential category weight
and phantom maps.
The essential category weight of a map f: X --> Y is
the least N such that fg is nullhomotopic whenever
g: Z --> X is a map with cat(Z) < N + 1. We write
E(f) > N - 1 in this case. A map has infinite
essential category weight ( E(f) = \infty ) if there
is no such N. The appendix to this paper contains a
brief summary of the main results on essential category
weight.
It is not hard to see that any map with E(f) = \infty
is a phantom map. We give examples to show that the
reverse is not always true: there are phantom maps f
with E(f) = 1. We also show that in some cases, all
the phantom maps f: X --> Y have E(f) = \infty.
We are able to adapt many of the results of the theory
of phantom maps to give us results about maps with
E(f) = \infty.
Finally, we use the connections between essential
category weight and phantom maps to answer a question
(asked by McGibbon) about phantom maps,
---------------------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
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/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.
------- End of forwarded message -------