Subject: hopf
From: mhovey@wesleyan.edu
Date: Fri, 7 Apr 2006 11:03:12 -0400 (EDT)
There are 4 new papers this time, from Blanc-Johnson-Turner,
Clarke-Crossley-Whitehouse, Muro-Tonks, Ziemianski.
I also wanted to say that in my paper of last time, there is an
isomorphism between the completed E(n)-cohomology of X and Hom from the
E(n)-homology of M_n X to an appropriate module. This isomorphism was
known before to Greenlees, Hopkins, Sadofsky, and others, though it does
not appear to be in print. The version of the paper now on the archive
reflects that.
Mark Hovey
New papers appearing on hopf between 3/1/06 and 4/7/06
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Blanc-Johnson-Turner/rdpa
Title: On Realizing Diagrams of Pi-algebras
Authors: David Blanc, Mark W. Johnson, and James M. Turner
Abstract:
Given a diagram of Pi-algebras (graded groups equipped with an action
of the primary homotopy operations), we ask whether it can be realized
as the homotopy groups of a diagram of spaces. The answer given here is in
the
form of an obstruction theory, of somewhat wider application,
formulated in terms of generalized Pi-algebras. This extends a
program begun by Dwyer, Kan, and Stover to study the realization of a
single Pi-algebra. In particular, we explicitly analyze the simple
case of a single map, and provide a detailed example, illustrating the
connections to higher homotopy operations.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Clarke-Crossley-Whitehouse/ccwDiscrete
The discrete module category for the ring of K-theory operations
Francis Clarke, Martin Crossley, Sarah Whitehouse
We study the category of discrete modules over the ring of degree zero
stable operations in p-local complex K-theory. We show that the p-local
K-homology of any space or spectrum is such a module, and that this
category is isomorphic to a category defined by Bousfield and used in
his work on the K-local stable homotopy category (Amer. J. Math., 1985).
We also provide an alternative characterisation of discrete modules as
locally finitely generated modules.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Muro-Tonks/1tK3
Title:The 1-type of a Waldhausen K-theory spectrum
Authors: Fernando Muro and Andrew Tonks
Abstract: We give a small functorial algebraic model for the 2-stage
Postnikov section of the K-theory spectrum of a Waldhausen category and
use our presentation to describe the multiplicative structure with
respect to biexact functors.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Ziemianski/DI4Rep
TITLE:
A faithful unitary representation of the 2-compact group DI(4)
AUTHOR:
Krzysztof Ziemianski
ABSTRACT:
We construct a monomorphism from the $2$-compact group $DI(4)$ into a
$2$-compact unitary group.
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