--------------------------------------------------------------------
4 new papers this month, from Arone-Dwyer-Lesh, Bendersky-DavisD,
Karoubi, and Wuethrich.  

                  Mark Hovey

New papers appearing on hopf between 5/14/07 and 6/8/07

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Arone-Dwyer-Lesh/LoopStructuresTaylorTowers

Title
Loop structures in Taylor towers

Authors
G. Z. Arone, W. G. Dwyer, K. Lesh

Kerchof Hall, U. of Virginia, P.O. Box 400137, Charlottesville VA 22904 USA
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556
Department of Mathematics, Union College, Schenectady, NY 12308

Abstract
We study spaces of natural transformations between homogeneous
functors in Goodwillie's calculus of homotopy functors and in
Weiss's orthogonal calculus.  We give a description of
such spaces of natural transformations in terms of the homotopy
fixed point construction. Our main application is a delooping
theorem for connecting maps in the Goodwillie tower of the identity
and in the Weiss tower of BU(V). The interest in such deloopings
stems from conjectures made by the first and the third author
in a 2007 paper that these towers provide a source of
contracting homotopies for certain projective chain complexes
of spectra.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bendersky-DavisD/DW2

v1-periodic homotopy groups of the Dwyer-Wilkerson space

Martin Bendersky
Donald M. Davis

Abstract:
The Dwyer-Wilkerson space DI(4) is the only exotic 2-compact group.
We compute its v1-periodic homotopy groups.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Karoubi/Karoubi

Cochaines quasi-commutatives en Topologie Algebrique

Max Karoubi

Abstract : We describe a new category of "quasi-commutative" DGA's ,
called D*, where the product is "almost" commutative : it is commutative
on a subcomplex of C = D* tensor D* (with some axioms). To each
simplicial set (or even ringed space) we associate a quasi-commutative
DGA, from which we recover the homotopy type and are able to describe an
explicit procedure to "compute" homotopy groups and cohomology
operations. The basic idea of the construction is to use difference
calculus, instead of differential calculus as in Sullivan's
theory.  This paper is an extension of ideas posted in the Archives
a few years ago under the title "Methodes quantiques en Topologie
Algebrique". However, the point of view is simpler and the proofs are
now complete. It is going to appear in the Quarterly Journal of Pure and
Applied Math.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Wuethrich/thickenings_final

Title:   Infinitesimal thickenings of Morava K-theories (final version)
         
Author:  Samuel Wuethrich

AMS classification number: 55P42, 55P43; 55U20, 55N22
arXive submission number:  math.AT/0607110

Comments:

25 pages. Final version, to appear in J. Pure Appl. Algebra. 
Contents of former section 5 mostly rewritten and reorganized 
into two sections; some minor corrections and changes

Abstract: 

A. Baker has constructed certain sequences of cohomology theories 
which interpolate between the Johnson-Wilson and the Morava 
K-theories. We realize the representing sequences of spectra as 
sequences of MU-algebras. Starting with the fact that the spectra 
representing the Johnson-Wilson and the Morava K-theories admit 
such structures, we construct the sequences by inductively 
forming singular extensions. Our methods apply to other pairs of 
MU-algebras as well.


 -----------------