Subject: new Hopf listings
From: Mark Hovey
Date: 15 Jul 2000 06:25:00 -0400
13 new papers this time.
Mark Hovey
New papers appearing on hopf between 6/16/00 and 7/16/00.
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/AlAgl-Brown-Steiner/multipleca
t
Multiple categories: the equivalence of a globular and a cubical
approach
Fahd A. A. Al-Agl, Ronald Brown, Richard Steiner
math.CT/0007009
Fahd A. A. Al-Agl\\Um-Alqura University,\\
Makkah\\Saudi Arabia
Ronald Brown, \\ School of Informatics, \\ Mathematics Division, \\ University o
f
Wales,\\ Bangor, Gwynedd LL57 1UT, \\ United Kingdom.
Richard Steiner, \\ Department of Mathematics, \\ University of
Glasgow, \\University Gardens, \\ Glasgow G12 8QW
\\ United Kingdom
r.brown@bangor.ac.uk
r.steiner@maths.gla.ac.uk
We show the equivalence of two kinds of strict multiple category,
namely the well known globular omega-categories, and the cubical
omega-categories with connections.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arkowitz-Strom/TrivModF
Homotopy Classes that are Trivial Mod F
Martin Arkowitz (Martin.Arkowitz@Dartmouth.edu)
Jeffrey Strom (Jeffrey.Strom@Dartmouth.edu)
Dartmouth College
If F is a collection of topological spaces, then a homotopy class \alpha
in [X,Y] is called F-trivial if
\alpha _* = 0: [A,X] --> [A,Y]
for all A in F. In this paper we study the collection Z_{F}(X,Y) of all
F-trivial homotopy classes in [X,Y] when F = S, the collection of
spheres, F = M, the collection of Moore spaces, and F = \Sigma, the
collection of suspensions. Clearly
Z_{\Sigma}(X,Y) \subseteq Z_{\M}(X,Y) \subseteq Z_{\S}(X,Y),
and we find examples of {\it finite complexes} X and Y for which these
inclusions are strict. We are also interested in Z_{F}(X) = Z_{F}(X,X)
which under composition has the structure of a semi-group with zero. We
show that if X is a finite dimensional complex and F = S, M or \Sigma,
then the semi-group Z_{F}(X) is nilpotent. More generally, the
nilpotency of Z_{F}(X) is bounded above by the F-killing length of X, a
new numerical invariant which equals the number of steps it takes to
make X contractible by successively attaching cones on wedges of spaces
in F, and this in turn is bounded above by the F-cone length of X. We
then calculate or estimate the nilpotency of Z_{F}(X) when F = S, M or
\Sigma for the following classes of spaces: (1) projective spaces (2)
certain Lie groups such as SU(n) and Sp(n). The paper concludes with
several open problems.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arlettaz/Arlettaz-survey
Title: Algebraic K-theory of rings from a topological viewpoint
Author: Dominique Arlettaz
Dominique Arlettaz, Institut de math\'ematiques,
Universit\'e de Lausanne, CH-1015 Lausanne, Switzerland
dominique.arlettaz@ima.unil.ch
Abstract: This paper is a long survey providing the basic definitions of
the algebraic K-theory of rings and an overview of the main classical
theorems which have been obtained by arguments from algebraic topology
(in particular by using methods from stable homotopy theory, group
cohomology and Postnikov theory). It will appear in Publicacions
Matem\`atiques.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arlettaz-Ausoni-Mimura-Yagita/
Arlettaz-A-M-Y
Title: Integral cohomology and Chern classes of the special linear group over
the ring of integers
Author1: Dominique Arlettaz
Author2: Christian Ausoni
Author3: Mamoru Mimura
Author4: Nobuaki Yagita
Author1: Dominique Arlettaz, Institut de math\'ematiques,
Universit\'e de Lausanne, CH-1015 Lausanne, Switzerland
Author2: Christian Ausoni, Departement Mathematik, HG, ETH-Zentrum, 8092
Z\"urich, Switzerland
Author3: Mamoru Mimura, Department of Mathematics, Faculty of Science, Okayama
University, Okayama, Japan 700
Author4: Nobuaki Yagita, Faculty of Education, Ibaraki University, Mito,
Ibaraki, Japan
E-mail1: dominique.arlettaz@ima.unil.ch
E-mail2: ausoni@math.ethz.ch
E-mail3: mimura@math.okayama-u.ac.jp
E-mail4: yagita@mito.ipc.ibaraki.ac.jp
Abstract: This paper is devoted to the complete calculation of the
additive structure of the 2-torsion of the integral cohomology of the
infinite special linear group SL(Z) over the ring of integers Z. This
enables us to determine the best upper bound for the order of the Chern
classes of all integral and rational representations of discrete groups.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Casacuberta-Scherer/casasche
Homological localizations preserve 1-connectivity
by Carles Casacuberta and Jerome Scherer
Universitat Autonoma de Barcelona Universite de Lausanne
casac@mat.uab.es jerome.scherer@ima.unil.ch
To appear in Contemporary Mathematics, Proceedings of the 1999
Arolla Conference on Algebraic Topology.
Every generalized homology theory $E$ yields a localization functor $L$
that sends the $E$-equivalences to homotopy equivalences. We prove that
if $X$ is any $1$-connected space, then $LX$ is also $1$-connected, for
every generalized homology theory $E$. This is deduced from a result by
Hopkins and Smith stating that if $K(\Z,2)$ is $E$-acyclic then $E$ is
trivial.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Dugger/ddpres
Title: Combinatorial Model Categories Have Presentations
Author: Daniel Dugger
Purdue University
West Lafayette, IN 47906
Email: ddugger@math.purdue.edu
We show that every combinatorial model category can be obtained---up
to Quillen equivalence---by localizing a model category of diagrams of
simplicial sets. This says that any combinatorial model category can
be built up from a category of `generators' and a set of `relations'
---i.e., any combinatorial model category has a presentation.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Dugger/dduniv
Title: Universal Homotopy Theories
Author: Daniel Dugger
Address:
Purdue University
West Lafayette, IN 47906
Email: ddugger@math.purdue.edu
Abstract: Given a small category C, we show that there is a universal
way of expanding C into a model category, essentially by formally
adjoining homotopy colimits. The technique of localization becomes a
method for imposing `relations' into these universal gadgets. The
paper develops this formalism and also discusses various applications,
for instance to the study of homotopy colimits, the Dwyer-Kan theory
of framings, and to the homotopy theory of schemes.
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Goebel-Rodriguez-Shelah/locsim
ple
TITLE: Large localizations of finite simple groups
AUTHORS: Ruediger Goebel, Jose L. Rodriguez, and Saharon Shelah
R.Goebel@uni-essen.de, jlrodri@mat.uab.es, shelah@math.huji.ac.il
ABSTRACT:
A group homomorphism $\eta: H\to G$ is called a localization of $H$ if
every homomorphism $\varphi : H\to G$ can be `extended uniquely' to a
homomorphism $\Phi :G\to G$ in the sense that $\Phi \eta = \varphi$.
Libman showed that a localization of a finite group need not be finite.
This is exemplified by a well-known representation $A_n\to SO_{n-1}(\R)$
of the alternating group $A_n$, which turns out to be a localization for
$n$ even and $n\geq 10$. Dror Farjoun asked if there is any upper bound
in cardinality for localizations of $A_n$. In this paper we answer this
question and prove, under the generalized continuum hypothesis, that
every non abelian finite simple group $H$, has arbitrarily large
localizations. This shows that there is a proper class of distinct
homotopy types which are localizations of a given Eilenberg--Mac Lane
space $K(H,1)$ for any non abelian finite simple group $H$.
9.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Mandell/finite
Equivariant p-adic Homotopy Theory
Michael A. Mandell
mandell@math.uchicago.edu
Let G be a finite group. We show that the cochain functor with
coefficients in \FPbar is an equivalence between the p-adic
G-equivariant homotopy category of finite type nilpotent G-spaces
and a full subcategory of the homotopy category of diagrams of \einf
\FPbar-algebras indexed on the orbit category of G.
This turns out to be an easy consequence of Elmendorf's Theorem and
Kan's work on diagrams in closed model categories plus the equivalence
in the nonequivariant context.
10.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Morava/PGGravity
Title: Pretty Good Gravity
Author: Jack Morava
(not yet on xxx, but will be soon)
Address: Dept. of Mathematics, the Johns Hopkins Uniperversity
e-mail address: jack@math.jhu.edu
Abstract: A theory of topological gravity is a homotopy-theoretic
representation of the Segal-Tillmann topologification of a two-category
with cobordisms as morphisms. This note describes a relatively accessible
example of such a thing, suggested by the wall-crossing formulas of
Donaldson theory.
[This is a writeup of a talk at the RIMS Symposium on algebraic geometry
and integrable systems related to string theory, June 12-16, 2000.]
11.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Ravenel/first
Title of paper: The first Adams-Novikov differential for the spectrum T(m)
Author: Douglas C. Ravenel
Address of Author: University of Rochester, Rochester, NY 14627
Email address of author: drav@math.rochester.edu
Abstract: There are p-local spectra T(m) with
$BP_{*}(T(m))=BP_{*}[t_{1},\dots ,t_{m}]$. In this paper we determine
the first nontrivial differential in the Adams--Novikov spectral
sequence for each of them for p odd. For m=0 (the sphere spectrum)
this is the Toda differential, whose source has filtration 2 and whose
target is the first nontrivial element in filtration 2p+1. The same
goes for m=1, and for larger m the target is $v_2$ times the first
such element. The proof uses the Thomified Eilenberg-Moore spectral
sequence.
12.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Ravenel/micro
Title of paper: The microstable Adams-Novikov spectral sequence
Author: Douglas C. Ravenel
Address of Author: University of Rochester, Rochester, NY 14627
Email address of author: drav@math.rochester.edu
Abstract: In the Adams--Novikov spectral sequence one considers Ext
groups over the Hopf algebroid $\Gamma =BP_{*}(BP)$. There are spectra
$T(m)$ with $BP_{*} (T (m))=BP_{*}[t_{1},...,t_{m}]$, which leads
one to replace $\Gamma $ by $\Gamma (m+1)=\Gamma / (t_{1},...
,t_{m})$. The corresponding Ext groups have certain structural
features that are independent of $m$. In this paper we set up an
algebraic framework for studying the limit as $m \to \infty $. In
particular there is an analog of the chromatic spectral sequence in
which the Morava stabilizer group gets replaced by an infinitesimal
analog, hence the title.
13.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/SmithL/koszulii
I can't read the abstract of this file, but I think this is not Larry's
fault. Clarence is out of town though, and I am about to be, so I
wanted to announce it now. It has to do with invariant theory of Z/p
acting on a polynomial ring F[V]. The detailed abstract will appear
next time.
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