Subject: new Hopf listings
Date: 24 Oct 2003 09:24:55 -0400
From: Mark Hovey
Reply-To: mhovey@wesleyan.edu
To: dmd1@lehigh.edu
10 new papers this time, from Dugger-Isaksen, Flores, Gaudens,
Kitchloo-Wilson, Klein, LinJP, Luo, Nam, Sauvageot, and Schwede.
Mark Hovey
New papers appearing on hopf between 9/26/03 and 10/24/03
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Dugger-Isaksen/motcell
Title: Motivic cell structures
Authors: Daniel Dugger and Daniel C. Isaksen
Authors' e-mail address: ddugger@math.uoregon.edu and isaksen@math.wayne.edu
Abstract:
An object in motivic homotopy theory is called cellular if it can be
built out of motivic spheres using homotopy colimit constructions. We
explore some examples and consequences of cellularity. We explain why
the algebraic K-theory and algebraic cobordism spectra are both
cellular, and prove some Kunneth theorems for cellular objects.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Flores/draft1
NULLIFICATION AND CELLULARIZATION OF CLASSIFYING SPACES OF FINITE GROUPS
by RAM'ON J. FLORES
Departamento de Matem'aticas, Universidad Aut'onoma de Barcelona,
E-08193 Bellaterra, Spain
E-mail address: ramonj@mat.uab.es
Mathematical subject classification: 55P20, 55P80.
Abstract. In this note we discuss the effect of the BZ/p-nullification
and the BZ/p-cellularization functors over classifying spaces of finite
groups, and we compare them with the corresponding ones with regard to
Moore spaces, that have been intensively studied in the last years. We
describe the BZ/p- nullification of BG by means of a Postnikov
fibration, and we classify all finite groups G for which BG is
BZ/p-cellular. In particular, we relate the effect these
(co)localizations have over the fundamental group with the analogous
functors in the category of groups.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Gaudens/bocksteinnul
Title: A remark on N. Kuhn's unbounded strong realization conjecture
Author(s): Gerald Gaudens
Author's e-mail address: gaudens@math.univ-nantes.fr
AMS classification number: 55S10; 57S35
Abstract:
N. Kuhn has given several conjectures on the special features satisfied
by the singular cohomology of topological spaces with coefficients in a
finite prime field, as modules over the Steenrod algebra. The so-called
Realization conjecture was solved in special cases By N. Kuhn and in
complete generality by L. Schwartz. The more general Strong realization
conjecture has been settled at the prime 2, as a consequence of the work
of L. Schwartz, and the subsequent work of F.-X. Dehon and the
author. In this note, we are interested in the even more general
Unbounded strong realization conjecture. We shall prove that it holds at
the prime $2$ for the class of spaces whose cohomology has a trivial
Bockstein action in high degrees.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Kitchloo-Wilson/kitchloo-wilson
Title:
On fibrations related to real spectra
Authors:
Nitu Kitchloo and W. Stephen Wilson
E-mail addresses:
nitu@math.jhu.edu, wsw@math.jhu.edu
Address:
Department of Mathematics
Johns Hopkins University
Baltimore, Maryland 21218
Abstract:
We consider real spectra, collections of Z/(2)-spaces
indexed over Z direct sum Z_\alpha with compatibility
conditions. We produce fibrations connecting the
homotopy fixed points and the spaces in these spectra.
We also evaluate the map which is the analogue of the
forgetful functor from complex to reals composed with
complexification. Our first fibration is used to connect
the real 2^{n+2}(2^n-1)-periodic Johnson-Wilson spectrum
ER(n) to the usual 2(2^n-1)-periodic Johnson-Wilson
spectrum, E(n). Our main result is the fibration
\Sigma^{\lambda(n)} ER(n) -> ER(n) -> E(n), where
\lambda(n) = 2^{2n+1}-2^{n+2}+1.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Klein/embclass
Title: On embeddings in the sphere
Author: John R. Klein
Author's e-mail address: klein@math.wayne.edu
Abstract: We consider embeddings of a finite complex in a sphere. We
give a homotopy theoretic classification such embeddings in a wide
range.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/LinJP/Lin=HspaceAnalog1
(This abstract was sent in dvi form; the program we use to convert is
not perfect).
H-spaces analogous to E8 mod 3
Dedicated to the memory of Masahiro Sugawara
James P. Lin
Department of Mathematics
University of California, San Diego
La Jolla, CA 92093-0112, U.S.A.
email:jimlin@euclid.ucsd.edu
Abstract: Let p be an odd prime. Let X0 be a finite, p-local, simply
connected homotopy associative H-space. Suppose H* (X0; Zp) contains the
subalgebra
Zp [x0,_z0]_xp p(r0, P1 r0, Pp P1 r0, y0)
0, z0
satisfying z0 = Pp x0 = Q0Pp P1 r0, Pp P1 r0 = P1 y0 for r0 2 H3 (X0;
Zp). The only known examples occur for p = 3 and involve the Lie group
E8. In this note we prove that if X0 exists, then p must be 3. Thus
there are no homotopy associative H-space analogues of E8mod 3 for
primes bigger than 3.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Luo/pre
(This is an updated version)
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.
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/Nam/transfer
Title : Transfert alg'ebrique et repr'esentation modulaire du groupe
lin'eaire
Author : Tran Ngoc Nam
Author's e-mail address : trngnam@hotmail.com
Author's mailing address : LAGA, Universit'e Paris 13, 93430 Villetaneuse,
France
Abstract : On se propose de d'eterminer la dimension d'une
repr'esentation du groupe lin'eaire d'efinie par un sous-espace
vectoriel de l'alg`ebre `a puissances divis'ees, d'expliciter
l'image du transfert alg'ebrique en degr'e g'en'erique et celle du
transfert alg'ebrique quadruple, d'identifier les ind'ecomposables
de degr'e pair de l'alg`ebre polynomiale `a 4 variables, vue comme
module sur l'alg`ebre de Steenrod mod 2.
9.
http://hopf.math.purdue.edu/cgi-bin/generate?/Sauvageot/thesis
STABILISATION DES COMPLEXES CROISES
Orin R. Sauvageot
orin.sauvageot@epfl.ch
Ecole Polytechnique Federale de Lausanne
Institute of Mathematics
This is my PhD thesis in FRENCH, 158 pages. The graphic files
C-tensor-I.eps, pi-delta-4.eps and pi-xc.eps are included in the zip
archives thesis-print.dvi.zip and thesis-screen.dvi.zip.
(Note from Mark; you should get these eps files individually if you get
the dvi file. The file thesis.dvi is thesis-print.dvi;
thesis-screen.dvi is in case you have trouble viewing the diagrams in
thesis.dvi on your screen. The files thesis.ps and thesis.pdf already
have the eps files embedded)
Abstract
In this doctoral thesis we present a stabilization of the category of
crossed complexes. Our work is motivated by the difficulty one has in
performing algebraic calculations in Boardman's stable homotopy
category, since products and actions are defined only up to homotopy in
the underlying category of spectra, as defined by Bousfield and
Friedlander. To correct this lack of precision, a number of new models
of the stable homotopy category have been developed in which algebraic
constructions are exactly defined. One such model is the category of
symmetric spectra on simplicial sets, the manipulation of which is still
not easy, however.
The idea behind this thesis is to stabilize the category of crossed
complexes, as it is an interesting approximation to the category of
simplicial sets, reflecting certain, though not all, nonabelian
homotopical information concerning simplicial sets. We have stabilized
it according to the procedure codified in Hovey's "Spectra and symmetric
spectra in general model categories".
Stabilization requires that the category of crossed complexes satisfies
certain properties. We have succeeded in proving these properties, in
each case establishing a previously unknown result. For example, we
have shown that it is cofibrantly generated and that it is a symmetric
monoidal model category. Furthermore we have verified that it is a
proper, cellular category. In proving the properness we have answered
an open question posed by Brown and Golasinski. In the course of
establishing these properties we have established a nonabelian version
of the 5-Lemma.
A crossed complex is a generalization of a chain complex of abelian
groups. We have shown, however, that the stabilization of crossed
complexes is homotopy equivalent to that of the category of chain
complexes. On the other hand, the situation of unpointed crossed
complexes is different, and it is very likely that their stabilization
is not that of chain complexes. In order to argue so, we have
constructed an innovative simplicial model of the Hopf map. It remains
then to give a topological meaning to an unpointed stabilization. An
attempt of answer is sketched.
10.
http://hopf.math.purdue.edu/cgi-bin/generate?/Schwede/Morita
Title: Morita theory in abelian, derived and stable model categories
Author: Stefan Schwede
e-mail address: sschwede@math.uni-muenster.de
This is a survey paper, based on lectures given at the
Workshop on "Structured ring spectra and their applications"
which took place January 21-25, 2002, at the University of Glasgow.
The term `Morita theory' is usually used for results concerning
equivalences of various kinds of module categories.
We focus on the covariant form of Morita theory, so the basic question is:
When do two `rings' have `equivalent' module categories ?
We discuss this question in different contexts and
illustrate it by examples:
(Classical) When are the module categories of two rings
equivalent as categories ?
(Derived) When are the derived categories of two rings
equivalent as triangulated categories ?
(Homotopical) When are the module categories of two ring spectra
Quillen equivalent as model categories ?
There is always a related question, which is in a sense more general:
What characterizes the category of modules over a `ring' ?
The answer is, mutatis mutandis, always the same: modules over a `ring'
are characterized by the existence of a `small generator', which
plays the role of the free module of rank one.
The precise meaning of `small generator' depends on the context,
be it an abelian category, a derived category or a stable model category.
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