Subject: new Hopf listings
From: Mark Hovey
Date: 11 Nov 2005 08:43:11 -0500
There are 7 new papers this time, from Bartels-Reich, Bousfield,
Fausk-Isaksen (2), Neusel, Neusel-Sezer, and Siebenmann.
Mark Hovey
New papers appearing on hopf between 10/1/05 and 11/11/05
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bartels-Reich/erb
Title: Coefficients for the Farrell-Jones Conjecture
Authors: Arthur Bartels, Holger Reich
Author's e-mail address: bartelsa@math.uni-muenster.de,
reichh@math.uni-muenster.de
Abstract:
We introduce the Farrell-Jones Conjecture with coefficients in
an additive category with G-action. This is a variant of the
Farrell-Jones Conjecture about the algebraic K- or L-Theory of
a group ring RG. It allows to treat twisted group rings and crossed
product rings. The conjecture with coefficients is stronger than
the original conjecture but it has better inheritance properties.
Since known proofs using controlled algebra carry over to the
set-up with coefficients we obtain new results about the original
Farrell-Jones Conjecture. The conjecture with coefficients implies
the fibered version of the Farrell-Jones Conjecture.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bousfield/kunneth
Title: Kunneth theorems and unstable operations in 2-adic KO-cohomology
Author: A.K. Bousfield
E-mail: bous@uic.edu
AMS classifications: 55N15,55S25,55U25
Abstract: We develop Kunneth theorems and obtain detailed results on
unstable operations in 2-adic KO-cohomology and, more generally, in
united 2-adic K-cohomology. These results are needed for work on the
K-localizations of H-spaces at the prime 2 and should be of independent
interest. Our proofs of relations for unstable operations rely on
Atiyah's Real K-theory and on a convenient mod 2 simplification of
2-adic KO-cohomology.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Fausk-Isaksen/filtered
Title: Model structures on pro-categories
Authors: Halvard Fausk, Daniel C. Isaksen
E-mail: fausk@math.uio.no, isaksen@math.wayne.edu
AMS Classification: 55U35 Primary ; Secondary 55P91, 18G55
Abstract:
We introduce a notion of a filtered model structure and use this notion
to produce various model structures on pro-categories. This framework
generalizes several known examples. We give several examples, including
a homotopy theory for $G$-spaces, where $G$ is a pro-finite group. The
class of weak equivalences is an approximation to the class of
underlying weak equivalences.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Fausk-Isaksen/t-model
Title: T-model structures
Authors: Halvard Fausk and Daniel C. Isaksen
E-mail: fausk@math.uio.no, isaksen@math.wayne.edu
AMS Classification: Primary 55P42; Secondary 18E30, 55U35
Abstract:
For every stable model category $\mathcal{M}$ with a certain extra
structure, we produce an associated model structure on the pro-category
pro-$\mathcal{M}$ and a spectral sequence, analogous to the
Atiyah-Hirzebruch spectral sequence, with reasonably good convergence
properties for computing in the homotopy category of
pro-$\mathcal{M}$. Our motivating example is the category of
pro-spectra.
The extra structure referred to above is a t-model structure. This is a
rigidification of the usual notion of a t-structure on a triangulated
category. A t-model structure is a proper simplicial stable model
category $\mathcal{M}$ with a t-structure on its homotopy category
together with an additional factorization axiom.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Neusel/piotr
Connected Hopf algebras with Dixmier bases and infinite primary
decomposition
Mara D. Neusel
Mara.D.Neusel@ttu.edu
Abstract:
In this paper we study the existence of invariant primary decompositions
for algebras and modules over Hopf algebras. This is an update of the
previous preprint of Neusel-Wisniewski of the same title.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Neusel-Sezer/noether
The Noether map
AUTHORS: Mara D. Neusel (Texas Tech University),
M\"ufit Sezer (Bo\u gazici \"Universitesi)
EMAILS: mara.d.neusel@ttu.edu
mufit.sezer@boun.edu.tr
ABSTRACT:
Let $\rho: G\hra GL(n\/,\ \F)$ be a faithful representation of a finite
group $G$. In this paper we study the image of the associated Noether
map \[ \eta_G^G: \F[V(G)]^G \longrightarrow \F[V]^G\/. \] It turns out
that the image of the Noether map characterizes the ring of invariants
in the sense that its integral closure $\overline{\Im(\eta_G^G)}
=\F[V]^G$. This is true without any restrictions on the group,
representation, or ground field. Furthermore, we show that the Noether
map is surjective, i.e., its image integrally closed, if $V=\F^n$ is a
projective $\F G$-module. Moreover, we show that the converse of this
statement is true if $G$ is a $p$-group and $\F$ has characteristic $p$,
or if $\rho$ is a permutation representation. We apply these results and
obtain upper bounds on the Noether number and the Cohen-Macaulay defect
of $\F[V]^G$. We illustrate our results with several examples.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Siebenmann/Schoen-02Sept2005
The Osgood-Schoenflies Theorem Revisited
by Laurent Siebenmann
Math'ematique, B^at. 425, Universit'e de Paris-Sud, 91405-Orsay, France
http://topo.math.u-psud.fr/~lcs/contact
This retrospective article presents an elementary, and hopefully direct
and clear, geo- metric proof of what is usually called the (classical
planar) Schoenflies Theorem; it is stated as (ST) in x4 below _ with
mention of its early history, including W.F. Osgood's rarely cited
contributions. This (ST) is essentially the fact _ surprising in view
of known fractal curves _ that every compact subset of the cartesian
plane R2 that is homeomorphic to the circle S1, is necessarily the
frontier in R2 of a set homeomorphic to the 2-disk. Beware that the
`Generalized Schoenflies theorem' of B. Mazur [Maz] and M. Brown
[Brow1] _ proved five decades later and valid in all dimensions _ does
not imply (ST) since it assumes a condition of flatness (or local
flatness [Brow2]).
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