Subject: new Hopf listings
From: Mark Hovey
Date: 25 Jan 2000 15:26:10 -0500
7 new papers this time.
Mark Hovey
New papers uploaded to hopf between 1/2/00 and 1/25/00.
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Anderson-DavisJ/MacPherson
Title: Mod 2 Cohomology of Combinatorial Grassmannians
Authors: Laura Anderson and James F. Davis
Abstract: Matroid bundles, introduced by MacPherson, are combinatorial
analogues of real vector bundles. This paper sets up the foundations of
matroid bundles, and defines a natural transformation from isomorphism
classes of real vector bundles to isomorphism classes of matroid bundles,
as well as a transformation from matroid bundles to spherical
quasifibrations. The poset of oriented matroids of a fixed rank classifies
matroid bundles, and the above transformations give a splitting from
topology to combinatorics back to topology. This shows the mod 2
cohomology of the poset of rank k oriented matroids (this poset classifies
matroid bundles) contains the free polynomial ring on the first k
Stiefel-Whitney classes. The homotopy groups of this poset are related to
the image of the J-homomorphism from stable homotopy theory.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Dwyer-Wilkerson/center-calc/ce
nter-calc
Centers and Coxeter elements
by
W. G. Dwyer and C. W. Wilkerson
dwyer.1@nd.edu
wilker@math.purdue.edu
Abstract:
Suppose that $G$ is a connected compact Lie group. We show that
simple numerical information about the Weyl group of $G$ can be used
to obtain bounds, often sharp, on the size of the center of $G$.
These bounds are obtained with the help of certain Coxeter elements
in the Weyl group. Variants of the method use generalized Coxeter
elements and apply to $p$-compact groups; in this case a splitting theorem
emerges. The Lie group results are mostly known, but our arguments
have a conceptual appeal.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Hovey-Palmieri/quillen
Stably thick subcategories of modules over Hopf algebras
by Mark Hovey and John Palmieri
hovey@member.ams.org and palmieri@member.ams.org
We discuss a general method for classifying certain subcategories of the
category of finite-dimensional modules over a finite-dimensional
cocommutative Hopf algebra B. Our method is based on that of
Benson-Carlson-Rickard, who classify such
subcategories when B=kG, the group ring of a finite group G over
an algebraically closed field k. We get a similar classification when
B is a finite sub-Hopf algebra of the mod 2 Steenrod algebra, with
scalars extended to the algebraic closure of Z/2. Along the way,
we prove a Quillen stratification theorem for cohomological varieties of
modules over any B, in terms of quasi-elementary sub-Hopf algebras of
B.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Notbohm/bdi4
ON THE 2-COMPACT GROUP DI(4)
Author: D. Notbohm
Besides the simple connected compact Lie groups there exists one further
simple connected 2-compact group, constructed by Dwyer and Wilkerson,
the group $DI(4)$. The mod-2 cohomology of the associated classifying
space $BDI(4)$ realizes the rank 4 mod-2 Dickson invariants. We show
that mod-2 cohomology determines the homotopy type of the space $BDI(4)$
and that the maximal torus normalizer determines the isomorphism type of
$DI(4)$ as 2-compact group. We also calculate the set of homotopy
classes of self maps of $BDI(4)$.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Notbohm/orthogonal
A UNIQUENESS RESULT FOR ORTHOGONAL GROUPS AS 2-COMPACT GROUPS
D. Notbohm
Two connected compact Lie groups are isomorphic if and only if their
maximal torus normalizer are isomorphic. It is conjectured that this
result generalizes to p-compact groups. Here, we prove the generalization for
orthogonal groups $O(n)$, the special orthogonal groups $SO(2k+1)$ and
the spinor groups $Spin(2k+1)$ considered as 2-compact groups.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/SchwartzL/FK
Author: Lionel Schwartz
Title: La filtration de Krull de la categorie U et la cohomologie des espaces
Jan. 6, 2000
The present paper gives a proof of a conjecture of N. Kuhn : if the mod 2
cohomology of a space has finite Krull filtration in the category of unstable
modules, it has to be a locally finite unstable module.
Some technical assumptions are required.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/WuJ/newwgroup
Title of Paper: A braided simplicial group
Author(s): Jie Wu
Email address of Authors: matwuj@nus.edu.sg
Text of Abstract:
By studying braid group actions on Milnor's construction of the
1-sphere, we show that the general homotopy group of the 3-sphere
is the fixed set of the pure braid group action on a certain
combinatorially described group. We also give a certain representation
of higher differentials in the Adams spectral sequence for the
homotopy groups of the 2-sphere.
Comments are welcome.
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