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4 new papers this month, from Bendersky-Churchill, Hovey, Naumann, and
Zivaljevic.  

                  Mark Hovey

New papers appearing on hopf between 12/14/04 and 1/10/05

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bendersky-Churchill/NormalForms

Title: A spectral sequence approach to normal forms.

Authors: Martin Bendersky & Richard C. Churchill

Address: CUNY/Hunter College, Graduate Center
          New York, NY 10021

AMS Classification: 55T05, 34C20

Abstract:
    The theory of normal forms has been around since Poincare's time.
An incomplete list of applications are to vector fields,
Hamiltonians at equilibria, differential equations and singularity
theory. In general one tries to modify a given element in a Lie
algebra into a particularly useful form.  The algorithm that
performs the conversion (the normal form algorithm) can be a
formidable computation.  In this paper we generalize the notion of
normal form to that of an initially linear group representation.
In this general setting we are able to interpret the normal form
algorithm as a calculation of a particularly simple spectral
sequence.  As a consequence we show that various vector spaces
that appear in the process of carrying out the normal form
algorithm are invariants of the orbit of the group representation.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey/prod-spec-seq

The generalized homology of products

Mark Hovey 
Wesleyan University   

We construct a spectral sequence that computes the E-homology of a
product of spectra.  The E_{2}-term of this spectral sequence consists
of the right derived functors of product in the category of
E_{*}E-comodules, and the spectral sequence always converges (with a
horizontal vanishing line at E_{infty}) when E is the Johnson-Wilson
theory E(n) and each factor of the product is L_{n}-local.  We are able to
prove some results about the E_{2}-term of this spectral sequence; in
particular, we show that the E(n)-homology of a product of
E(n)-module spectra X^{\alpha} is just the comodule product of the
E(n)_{*}X^{\alpha}.  This spectral sequence is relevant to the
chromatic splitting conjecture.

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

Comodule categories and the geometry of the stack of formal groups
N. Naumann

We generalise recent results of M. Hovey and N. Strickland 
on comodule categories for Landweber exact algebras using the
formalism of algebraic stacks.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Zivaljevic/synergia

Title: Equipartitions of measures in R^4
Author: Rade Zivaljevic
AMS Class.: 52A39; 52C35; 55S40; 57R22; 57R91; 68P30
arXiv:math.CO/0412483 v1 December 2004

Address: Mathematical Institute SANU, Knez Mihailova 35/1, p.o. box 367
                                      11001 Belgrade
                                      Serbia and Montenegro

A measure in R^4 admits an equipartition by 4 hyperplanes, provided it
is symmetric with respect to a 2-dimensional, affine subspace L of R^4.
The computation is based on the Koschorke's exact singularity sequence
for groups of normal bordisms and the remarkable properties of the
essentially unique, balanced binary Gray code in dimension 4.

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