Subject: new Hopf listings
From: Mark Hovey
Date: 01 Jan 2007 11:45:05 -0500
There are 7 new papers this time, from Castellana-Crespo-Scherer,
Clement-Scherer, Colman, Maltsiniotis, Matthey-Pitsch-Scherer, Nakagawa,
and Ruiz.
Mark Hovey
New papers appearing on hopf between 12/7/06 and 1/1/07
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Castellana-Crespo-Scherer/covers
Title: On the cohomology of highly connected covers of finite
complexes
Authors: Natalia Castellana, Juan A. Crespo, and Jerome Scherer
Abstract: Relying on the computation of the Andre-Quillen homology
groups for unstable Hopf algebras, we prove that the mod p
cohomology of the n-connected cover of a finite H-space is always
finitely generated as algebra over the Steenrod algebra.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Clement-Scherer/exponent
Title: Homology exponents for H-spaces
Authors: Alain Clement and Jerome Scherer
Abstract: We say that a space X admits a homology exponent if
there exists an exponent for the torsion subgroup of the integral
homology. Our main result states that if an H-space of finite type
admits a homology exponent, then either it is, up to 2-completion,
a product of spaces of the form BZ/2^r, S1, K(Z,2), and K(Z,3),
or it has infinitely many non-trivial homotopy groups and
k-invariants. We then show with the same methods that simply
connected H-spaces whose mod 2 cohomology is finitely generated as
an algebra over the Steenrod algebra do not have homology
exponents, except products of mod 2 finite H-spaces with copies of
K(Z,2) and K(Z,3).
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Colman/ColmanHTG
Title of Paper: On the homotopy type of Lie groupoids
Author: Hellen Colman
Address of Author: Department of Mathematics, Wilbur Wright College,
4300 N. Narragansett Avenue, Chicago, IL 60634 USA
Text of Abstract:
We propose a notion of groupoid homotopy for generalized maps. This
notion of groupoid homotopy generalizes the notions of natural
transformation and strict homotopy for functors. The groupoid homotopy
type of a Lie groupoid is shown to be invariant under Morita
equivalence. As an application we consider orbifolds as groupoids and
study the orbifold homotopy between orbifold maps induced by the
groupoid homotopy.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Maltsiniotis/adjquill
Title: Le theoreme de Quillen, d'adjonction des foncteurs derives,
revisite
Author: Georges MALTSINIOTIS
English Translation: math.AT/0611952
Address:
Université Paris 7 Denis Diderot
Case Postale 7012
2, place Jussieu
F-75251 PARIS CEDEX 05
Abstract:
The aim of this paper is to present a very simple original, purely
formal, proof of Quillen's adjunction theorem for derived functors, and
of some more recent variations and generalizations of this theorem. This
is obtained by proving an abstract adjunction theorem for "absolute"
derived functors. In contrast with all known proofs, the explicit
construction of the derived functors is not used.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Matthey-Pitsch-Scherer/Blochlift
Title: Generalized orientations and the Bloch invariant
Authors: Michel Matthey, Wolfgang Pitsch, and Jerome Scherer
Abstract: For compact hyperbolic 3-manifolds we lift the Bloch
invariant defined by Neumann and Yang to an integral class in
K_3(C). Applying the Borel and the Bloch regulators, one gets back
the volume and the Chern-Simons invariant of the manifold. We also
discuss the non-compact case, in which there appears a
Z/2-ambiguity.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Nakagawa/cohomologyE8
Title: The integral cohomology ring of E_8/T1 E_7
Author: Masaki Nakagawa
Address of author: Department of General Education,
Takamatsu National College of Technology,
355 Chokushi-cho, Takamatsu,
761-8058, Japan
Abstract:
The generalized flag manifolds are homogeneous spaces of the form G/C,
where G is a compact connected Lie group and C is the centralizer of a
torus in G. These homogeneous spaces play an important role in
algebraic topology, algebraic geometry and differential geometry. In
this paper, using the Borel presentation and a method due to Toda, we
determine the integral cohomology ring of a certain generalized flag
manifold which is a quotient space of the exceptional Lie group E8.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Ruiz/ar-gl-rv
Title: Exotic normal fusion subsystems of General Linear Groups.
Author: Albert Ruiz
Institution: Departament de Matematiques,
Universitat Autonoma de Barcelona,
08193 Cerdanyola del Valles,
Spain.
Abstract:
We classify the saturated fusion subsystems of index prime to $p$ of the
general linear group over $F_q$ over a Sylow $p$-subgroup, where $q$ is
a prime power prime to an odd prime $p$. In this classification we get
some of the exotic $p$-local finite groups discovered by C. Broto and
J. Moller as saturated fusion subsystems of the general linear group.
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