Subject: new Hopf listings
Date: 13 Nov 2002 09:29:35 +0000
From: nsthov01@newton.cam.ac.uk (M.A. Hovey)
Hopf received nine new papers in just nine days, so its time to announce
them again already. There are papers from Anton, Broto-Levi-Oliver,
Christensen-Dwyer-Isaksen, Jardine (3), and Strickland (3).
Also, I just recently found out that it seems to be impossible to put
files on Hopf using anonymous ftp. We are trying to fix this, but in
the meantime I suggest using the web form.
Mark Hovey
New papers appearing on hopf between 11/04/02 and 11/13/02
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Anton/elementary.invariant
Title of Paper: An elementary invariant problem and general linear group
cohomology restricted to the diagonal subgroup
Author: Marian F. Anton
AMS Classification numbers: 57T10, 20J05, 19D06, 55R40
Address of Author: University of Sheffield, Department of Pure Mathematics,
Hicks Building, Sheffield, S3 7RH, U.K.
Email address of Author: Marian.Anton@imar.ro
Conjecturally, for p an odd prime and R a certain ring of p-integers,
the stable general linear group GL(R) and the etale model for its
classifying space have isomorphic mod p cohomology rings. In particular,
these two cohomology rings should have the same image with respect to
the restriction map to the diagonal subgroup. We show that a strong
unstable version of this last property holds for any rank if p is
regular and certain homology classes for SL(2,R) vanish.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Broto-Levi-Oliver/blo-surv
The theory of $p$-local groups: a survey
by C. Broto, R. Levi, and B. Oliver
This paper is a survey of recent results by the three authors, results
which describe how the p-local fusion in a finite group G determines and
is determined by the homotopy type of the p-completion of its classifying
space BG. This connection then suggested to us the construction of
certain spaces (classifying spaces of ``p-local finite groups'' and
``p-local compact groups'') which have many of the same properties as have
p-completed classifying spaces of finite and compact Lie groups, and which
can be characterized in homotopy theoretic terms.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Christensen-Dwyer-Isaksen/obstruction
(This is an update)
Obstruction theory in model categories
J. Daniel Christensen, William G. Dwyer and Daniel C. Isaksen
MSC: 55S35, 55U35, 18G55 (primary); 18G30, 55P42 (secondary)
Department of Mathematics
University of Western Ontario
London, Ontario N6A 5B7
jdc@uwo.ca
Department of Mathematics
University of Notre Dame
South Bend, IN 46556
dwyer.1@nd.edu
Department of Mathematics
University of Notre Dame
South Bend, IN 46556
isaksen.1@nd.edu
Keywords: obstruction theory, closed model category, simplicial set,
spectrum
Many examples of obstruction theory can be formulated as the study
of when a lift exists in a commutative square. Typically, one of
the maps is a cofibration of some sort and the opposite map is a
fibration, and there is a functorial obstruction class that determines
whether a lift exists. Working in an arbitrary pointed proper model
category, we classify the cofibrations that have such an obstruction
theory with respect to all fibrations. Up to weak equivalence, retract,
and cobase change, they are the cofibrations with weakly contractible
target. Equivalently, they are the retracts of principal cofibrations.
Without properness, the same classification holds for cofibrations
with cofibrant source. Our results dualize to give a classification
of fibrations that have an obstruction theory.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/cubical2
Abstract: "Cubical homotopy theory: a beginning", by. J.F. Jardine
This paper gives a closed model structure for the category of cubical
sets, suitably defined, and displays an equivalence of the associated
homotopy category with the ordinary homotopy category of topological
spaces, or simplicial sets.
Cubical complexes appeared in the early descriptions of homology
theory and combinatorial homotopy theory in the middle of the
twentieth century, but development of the subject area effectively
stopped as simplicial sets became the dominant combinatorial model for
homotopy theory as a result of the work of Kan and later
Quillen. Cubical complexes have recently resurfaced as objects of
fundamental interest in Pratt's theory of higher dimensional automata
in concurrency theory.
Department of Mathematics
University of Western Ontario
London, Ontario N6A 5B7
Canada
URL: http://www.math.uwo.ca/~jardine/papers/
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/gen-shea
Abstract: "Generalised sheaf cohomology theory", by. J.F. Jardine
This is an expanded version of notes for a set of lectures given at
the Newton Institute during a NATO ASI Workshop entitled ``Homotopy
Theory of Geometric Categories'' on September 23 and 24, 2002. The
paper presents some of the basic features of the homotopy theory of
simplicial presheaves and the stable homotopy theory of presheaves of
spectra, and then displays their use in the course of giving an
outline of proof of Thomason's descent theorem for Bott periodic
K-theory, in the context of equivariant stable categories for
profinite groups.
Department of Mathematics
University of Western Ontario
London, Ontario N6A 5B7
Canada
URL: http://www.math.uwo.ca/~jardine/papers/
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/int-str
Abstract: "Intermediate model structures for simplicial presheaves",
by J.F. Jardine
This note (it is not really a finished paper) shows that any set of
cofibrations containing the standard set of generating projective
cofibrations determines a closed model structure on the category of
simplicial presheaves on a small Grothendieck site, for which the weak
equivalences are the local weak equivalences in the usual sense. A
condition is given for these new model structures to be cofibrantly
generated; this condition is met by Blander's local projective theory.
Department of Mathematics
University of Western Ontario
London, Ontario N6A 5B7
Canada
URL: http://www.math.uwo.ca/~jardine/papers/
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Strickland/mcurve
Multicurves and equivariant cobordism
Neil Strickland
55N20,55N22,55N91,14L05
Department of Pure Mathematics
University of Sheffield
Sheffield S3 7RH
UK
Let A be a finite abelian group. We set up an algebraic framework for
studying A-equivariant complex-orientable cohomology theories in terms
of a suitable kind of equivariant formal groups. We compute the
equivariant cohomology of many spaces in these terms, including
projective bundles (and associated Gysin maps), Thom spaces, and
infinite Grassmannians.
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/Strickland/rfg
Realising formal groups
Neil Strickland
55N20,55N22
Department of Pure Mathematics
University of Sheffield
Sheffield S3 7RH
UK
We show that a large class of formal groups can be realised
functorially by even periodic ring spectra.
9.
http://hopf.math.purdue.edu/cgi-bin/generate?/Strickland/st-csi
Common subbundles and intersections of divisors
Neil P. Strickland
55N20 14L05 14M15
Department of Pure Mathematics
University of Sheffield
Hicks Building
Hounsfield Road
Sheffield S3 7RH
UK
N.P.Strickland@sheffield.ac.uk
Let V_0 and V_1 be complex vector bundles over a space X. We use the
theory of divisors on formal groups to give obstructions in
generalised cohomology that vanish when V_0 and V_1 can be embedded in
a bundle U in such a way that the intersection of V_0 and V_1 has
dimension at least k everywhere. We study various algebraic universal
examples related to this question, and show that they arise from the
generalised cohomology of corresponding topological universal
examples. This extends and reinterprets earlier work on degeneracy
classes in ordinary cohomology or intersection theory.
---------------------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.
------- End of forwarded message -------