Subject: new Hopf listings
From: Mark Hovey
Date: 04 Jan 2006 11:58:43 -0500
There are 8 new papers this time, from Arone-Lesh, BrownR, Gutierrez,
Inoue-Yagita, Klein-Williams, Korbas, Lockridge, and Ziemianski
Mark Hovey
New papers appearing on hopf between 11/11/05 and 1/4/06
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Arone-Lesh/arone-lesh-press
Title:
Filtered spectra arising from permutative categories
Authors:
Gregory Arone
University of Virginia
Kathryn Lesh
Union College
Abstract: Given a special Gamma-category C satisfying some mild
hypotheses, we construct a sequence of spectra interpolating between
the spectrum associated to C and the Eilenberg-Mac Lane spectrum
HZ. Examples of categories to which our construction applies are: the
category of finite sets, the category of finite-dimensional vector
spaces, and the category of finitely-generated free modules over a
reasonable ring. In the case of finite sets, our construction recovers
the filtration of HZ by symmetric powers of the sphere spectrum. In
the case of finite-dimensional complex vector spaces, we obtain an
apparently new sequence of spectra, A_{m}, that interpolate between bu
and HZ. We think of A_{m} as a ``bu-analogue'' of the m'th symmetric
power of the sphere and describe far-reaching formal similarities
between the two sequences of spectra. For instance, in both cases the
m'th subquotient is contractible unless m is a power of a prime, and
in v_{k}-periodic homotopy the filtration has only k+2 nontrivial
terms. There is an intriguing relationship between the bu-analogues of
symmetric powers and Weiss's orthogonal calculus, parallel to the not
yet completely understood relationship between the symmetric powers of
spheres and the Goodwillie calculus of homotopy functors. We
conjecture that the sequence {A_{m}}, when rewritten in a suitable
chain complex form, gives rise to a minimal projective resolution of
the connected cover of $bu$. This conjecture is the bu-analogue of a
theorem of Kuhn and Priddy about the symmetric power filtration. The
calculus of functors provides substantial supporting evidence for the
conjecture.
This is a revision of a preprint previously submitted to Hopf.
The paper has been accepted for publication in
Journal für die reine und angewandte Mathematik (Crelle's Journal).
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR/PB-jordan
Title: Groupoids, the Phragmen-Brouwer Property, and the Jordan
Curve Theorem
Author: Ronald Brown
Author's e-mail address: r.brown at bangor.ac.uk
Author's mailing address: Mathematics Department, School of Informatics,
University of Wales, Bangor, Gwynedd LL57 1UT, UK
Author's web site: www.bangor.ac.uk/r.brown
Preprint: University of Wales Math Preprint 06.01
Abstract: We publicise a proof of the Jordan Curve Theorem which
relates it to the Phragmen-Brouwer Property, and whose proof uses the
van Kampen theorem for the fundamental groupoid on a set of base points.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Gutierrez/hlems
Homological localizations of Eilenberg-Mac Lane spectra
Javier J. Guti\'errez
We discuss the Bousfield localization $L_E X$ for any spectrum $E$
and any $HR$-module $X$, where $R$ is a ring with unit. Due to the
splitting property of $HR$-modules, it is enough to study the localization
of Eilenberg--Mac\,Lane spectra. Using general results about stable
$f$-localizations, we give a method to compute the localization of an
Eilenberg--Mac\,Lane spectrum $L_E HG$ for any spectrum $E$ and any
abelian
group $G$. We describe $L_E HG$ explicitly when $G$ is one of the
following:
finitely generated abelian groups, $p$-adic integers, Pr\"ufer groups,
and subrings of the rationals. The results depend basically on
the $E$-acyclicity patterns of the spectrum $H\Q$ and the spectrum
$H\Z/p$ for each prime $p$.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Inoue-Yagita/bpso
Title: The complex cobordism of BSOn
Authors: K.Inoue and N.Yagita
Abstract: In this paper, we compute MU(BSO(2n)) and show that it is
generated as an MU-algebra by Conner-Floyd Chern classes and one
2n-dimensional element. For the case BO(m) are still studied by
W.S.Wilson. We get the result by using (equivariant) stratification
methods introduced to compute Chow rings by Guillot, Molina, Vessozi and
Vistoli.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Klein-Williams/int-theoryI
Homotopical intersection theory, I.
by John R. Klein and E. Bruce Williams
Abstract:
We give a new approach to intersection theory. Our ``cycles'' are closed
manifolds mapping into compact manifolds and our ``intersections'' are
elements of a homotopy group of a certain Thom space. The results are
then applied in various contexts, including fixed point, linking and
disjunction problems. Our main theorems resemble those of Hatcher and
Quinn.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Korbas/cuplength
Title: Bounds for the cup-length of Poincare spaces and their applications
Author: Julius Korbas
AMS Classification numbers: Primary: 57N65; 55M30 Secondary: 53C30
Author's addresses: Department of Algebra, Geometry, and Mathematical
Education,
Faculty of Mathematics, Physics, and Informatics,
Comenius University,
Mlynska dolina,
SK-842 48 Bratislava 4,
Slovakia
or
Mathematical Institute, Slovak Academy of Sciences,
Stefanikova 49, SK-814 73 Bratislava 1, Slovakia
Abstract: Our main result offers a new (quite systematic) way of
deriving bounds for the cup-length of Poincare spaces over fields; we
outline a general research program based on this result. For the
oriented Grassmann manifolds, already a limited realization of the
program leads, in many cases, to the exact values of the cup-length and
to interesting information on the Lyusternik-Shnirel'man category.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Lockridge/gh
Title: The generating hypothesis in the derived category of R-modules.
Author: Keir H. Lockridge
Abstract: In this paper, we prove a version of Freyd's generating
hypothesis for triangulated categories: if D is a cocomplete
triangulated category and S is an object in D whose endomorphism ring is
graded commutative and concentrated in degree zero, then S generates (in
the sense of Freyd) the thick subcategory determined by S if and only if
the endomorphism ring of S is von Neumann regular. As a corollary, we
obtain that the generating hypothesis is true in the derived category of
a commutative ring R if and only if R is von Neumann regular. We also
investigate alternative formulations of the generating hypothesis in the
derived category. Finally, we give a characterization of the Noetherian
stable homotopy categories in which the generating hypothesis is true.
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/Ziemianski/SpinHtpReps
TITLE:
Homotopy representations of Spin(7) and SO(7) at prime 2
AUTHOR:
Krzysztof Ziemianski
ADDRESS:
Faculty of Mathematics, Informatics and Mechanics
Warsaw University
Banacha 2
02-097 Warszawa
POLAND
ABSTRACT:
A homotopy (complex) representation of a compact connected Lie group L
at prime p is a map from BL into the p-completion of the classifying
space of the unitary group. In this paper we give a partial
classification of homotopy representations of SO(7) and Spin(7) at prime
2. Motiviation for considering this problem is twofold: first, one may
hope that it would help to understand maps between classifying
spaces. Secondly, construction of a homotopy representation of Spin(7)
is a crucial step in the construction of a faithful representation of
the 2-compact group DI(4).
---------------------Instructions-----------------------------
To subscribe or unsubscribe to this list, send a message to Don Davis at
dmd1@lehigh.edu with your e-mail address and name.
Please make sure he is using the correct e-mail address for you.
To see past issues of this mailing list, point your WWW browser to
http://math.wesleyan.edu/~mhovey/archive/
If this doesn't work or is missing a few issues, try
http://www.lehigh.edu/~dmd1/algtop.html
which also has the other messages sent to Don's list.
To get the papers listed above, point your Web browser to the URL
listed. The general Hopf archive URL is
http://hopf.math.purdue.edu
There is a web form for submitting papers to Hopf on this site as well.
You should submit an abstract as well. Clarence has explicit
instructions for the form of this abstract: see
http://hopf.math.purdue.edu/new-html/submissions.html
In particular, your abstract is meant to be read by humans, so should be
as readable as possible. I reserve the right to edit unreadable
abstracts. You should then e-mail Clarence at wilker at math.purdue.edu
telling him what you have uploaded.
The largest archive of math preprints is at
http://arxiv.gov
There is an algebraic topology section in this archive. The most useful
way to browse it or submit papers to it is via the front end developed
by Greg Kuperberg:
http://front.math.ucdavis.edu
To get the announcements of new papers in the algebraic topology section
at the arXiv, send e-mail to math@arxiv.org with subject line "subscribe"
(without quotes), and with the body of the message "add AT" (without
quotes).
I am solely responsible for these messages---don't send complaints
about them to Clarence. Thanks to Clarence for creating and maintaining
the archive.