Subject: new Hopf listings
From: Mark Hovey
Date: 01 Mar 2006 08:58:23 -0500
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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