There are 4 new papers this time, from BrownR, DavisDaniel, DavisD, and
Hovey.
                  Mark Hovey

New papers appearing on hopf between 2/8/06 and 3/1/06

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR/bedlewo

Title: Three themes in the work of  Charles Ehresmann:
Local-to-global; Groupoids; Higher dimensions.

Author: Ronald Brown

AMS classification number: 01A60,53C29,81Q70,22A22,55P15

Expansion of an invited talk given to the 7th Conference on the
Geometry and Topology of Manifolds:  The Mathematical Legacy of
Charles Ehresmann,  Bedlewo 8.05.2005-15.05.2005 (Poland).

Abstract: This paper illustrates the themes of the title in terms
of: van Kampen type theorems for the fundamental groupoid;
holonomy and monodromy groupoids; and higher homotopy groupoids.
Interaction with work of the writer is explored.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/DavisDaniel/cplx2

Title: The E_2-term of the descent spectral sequence for continuous G-spectra
Author: Daniel G. Davis
Author's address: Purdue University

Abstract: Let {X_i} be a tower of discrete G-spectra, each of which is 
fibrant as a spectrum, so that X=holim_i X_i is a continuous G-spectrum, 
with homotopy fixed point spectrum X^{hG}. The E_2-term of the descent 
spectral sequence for \pi_*(X^{hG}) cannot always be expressed as 
continuous cohomology. However, we show that the E_2-term is always built 
out of a certain complex of spectra, that, in the context of abelian groups, 
is used to compute the continuous cochain cohomology of G with coefficients 
in lim_i M_i, where {M_i} is a tower of discrete G-modules.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/DavisD/CPcrabb4

Some new immersion results for complex projective space

Donald M. Davis 

Lehigh University, Bethlehem, PA 18015

Abstract:
We prove the following two new optimal immersion results for complex
projective space.

First, if n equiv 3 mod 8 but n not equiv 3 mod 64, and alpha(n)=7, then
CP^n can be immersed in R^{4n-14}.

Second, if n is even and alpha(n)=3, then CP^n can be immersed in R^{4n-4}.

Here alpha(n) denotes the number of 1's in the binary expansion of n.

The first contradicts a result of Crabb, who said that such an immersion
does not exist, apparently due to an arithmetic mistake.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey/injective-comod

Injective comodules and Landweber exact homology theories

Mark Hovey

Wesleyan University
Middletown, CT

We classify the indecomposable injective E(n)_{*}E(n)-comodules, where
$E(n)$ is the Johnson-Wilson homology theory.  They are suspensions of
the J_{n,r}, where J_{n,r} is the E(n)-homology of the rth monochromatic
piece M_{r} E(r) of E(r) and $0\leq r\leq n$.  The endomorphism ring of
J_{n,r} is the ring of operations in the completed E(r) theory; this
ring of operations is not really known so far as I know, though it is
closely related to the stabilizer group S_r.  An interesting
byproduct of this study is the isomorphism

E^{*}(X) = \Hom_{E(n)_{*}} (E(n)_{*}M_{n}X, K)

where E is completed E(n) theory and K is the n-fold desuspension of 

E(n)_{*}/I_{n}^{\infty}).


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