Subject: new Hopf listings
From: Mark Hovey
Date: 05 Jun 2000 03:49:01 -0400
9 new papers this time, including the Mahowald-Ravenel-Shick paper
returning the telescope conjecture to the community.
Mark Hovey
New papers uploaded to hopf between 4/9/00 and 6/4/00.
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem-Carlson-Karagueuzian-Milg
ram/hs
The Cohomology of the Sylow 2-Subgroup of the Higman-Sims Group
A. Adem
Mathematics Department
University of Wisconsin
Madison WI 53706
J. F. Carlson
Mathematics Department
University of Georgia
Athens GA 30602
D. B. Karagueuzian
Mathematics Department
University of Wisconsin
Madison WI 53706
R. James Milgram
Mathematics Department
Stanford University
Stanford CA 94305
Abstract
In this paper we compute the mod 2 cohomology of the Sylow
2-subgroup of the Higman--Sims group HS, one of the 26 sporadic
simple groups. We obtain its Poincare series as well as an
explicit description of it
as a ring with 17 generators and 79 relations.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem-Pakianathan/adpak
On the Cohomology of Central Frattini Extensions
Alejandro Adem and Jonathan Pakianathan
Mathematics Department
University of Wisconsin
Madison, Wisconsin, 53706
adem@math.wisc.edu, pakianat@math.wisc.edu
Abstract
In this paper we provide calculations for the mod p cohomology
of certain p-groups, using topological methods.
More precisely, we look at p-groups G defined as central extensions
1-> V -> G ->W ->1 of elementary abelian groups
such that the mod p reduction of G/[G,G] is W and
the defining k-invariants span the entire image of the
Bockstein. We show that if p>dim V-dim W+1, then the mod p cohomology
of G can be explicitly computed as an algebra.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Ausoni-Rognes/tcl_us
Title: Algebraic K-theory of topological K-theory
Author: Christian Ausoni
Author2: John Rognes
Email: ausoni@math.ethz.ch
Email2: rognes@math.uio.no
Abstract:
Let l_p = BP<1>_p be the p-complete connective Adams summand of
topological K-theory, and let V(1) be the Smith-Toda complex. For p>3 we
explicitly compute the V(1)-homotopy of the algebraic K-theory spectrum
of l_p. In particular we find that it is a free finitely generated module
over the polynomial algebra P(v_2), except for a sporadic class in degree
2p-3. Thus also in this case algebraic K-theory increases chromatic
complexity by one. The proof uses the cyclotomic trace map from algebraic
K-theory to topological cyclic homology, and the calculation is actually
made in the V(1)-homotopy of the topological cyclic homology of l_p.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Dwyer-Greenlees/CompleteTorsio
n
Complete modules and torsion modules
by
W. G. Dwyer and J. P. C. Greenlees
Suppose that $R$ is a ring and that $A$ is a chain complex over
$R$. Inside the derived category of differential graded $R$-modules
there are naturally defined subcategories of $A$-torsion objects and
of $A$-complete objects. Under a finiteness condition on $A$, we
develop a Morita theory for these subcategories, find conceptual
interpretations for some associated algebraic functors, and, in
appropriate commutative situations, identify the associated functors
as local homology or local cohomology. Some of the results are
suprising even in the case $R=Z$ and $A=Z/p$.
Addresses:
University of Notre Dame, Notre Dame, IN 46556, USA
dwyer.1@nd.edu
School of Mathematics and Statistics, Hicks Building, Sheffield S3 7RH. UK
j.greenlees@sheffield.ac.uk
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Kuhn/kuhnsplit
Stable Splittings and the Diagonal
Nicholas J. Kuhn
Department of Mathematics, University of Virginia, Charlottesville, VA 22903
njk4x@virginia.edu
AMS classification numbers: Primary 55P35; Secondary 55P42
Many approximations to function spaces admit natural stable splittings,
with a typical example being the stable splitting of a space C_d(X)
approximating Omega^d Sigma^d X. With an eye towards understanding cup
products in the cohomology of such function spaces, we describe how the
diagonal interacts with the stable splitting. The description involves
group theoretic transfers.
In an appendix independent of the rest of the paper, we use ideas from
Goodwillie calculus to show that such natural stable splittings are
unique, and discuss three different constructions showing their
existence.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Mahowald-Ravenel-Shick/telconj
Title: The triple loop space approach to the telescope conjecture
Authors: Mark Mahowald, Doug Ravenel, Paul Shick
Addresses: Northwestern University, University of Rochester, John Carroll
University
email: mark@math.mwu.edu, drav@harpo.cc.rochester.edu, shick@jcu.edu
AMS Classification: 55
Abstract: The purpose of this paper is to describe an unsuccessful
attempt to prove that the telescope conjecture is false for all
$n \ge 2$ and all primes $p$. At the time it was originally proposed
over 20 years ago, the telescope conjecture appeared to be the simplest
and most plausible statement about the relationship between two
different localization functors. We hope that the present paper will
show that this is no longer the case. We will set up a spectral sequence
converging to the homotopy of one of the two localizations (the
geometrically defined telescope) of a certain spectrum, and it will be
apparent that only a bizarre pattern of differentials would lead to the
known homotopy of the localization defined in terms of $BP$-theory.
While we cannot exclude such a pattern, it is certainly not favored by
Occam's razor.
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Mahowald-Ravenel-Shick/temss
Title: The Thomified Eilenberg-Moore spectral sequence
Authors: Mark Mahowald, Doug Ravenel, Paul Shick
Addresses: Northwestern University, University of Rochester, John Carroll
University
email: mark@math.mwu.edu, drav@harpo.cc.rochester.edu, shick@jcu.edu
AMS Classification: 55
Abstract: We construct a generalization of the Eilenberg-Moore
spectal sequence, which in some interesting cases turns out to be
a form the Adams spectral sequence. We apply the spectral sequence
to give a new construction of the $Z /p$-equivariant Adams spectral
sequence of Greenlees.
9.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/McAuley/revised-hilbert
This one has an abstract in .dvi form, so I do not include it.
The title is
A Proof of the Hilbert-Smith Conjecture
by Louis F. McAuley
(The Hilbert-Smith conjecture is the one about a topological group
having to be a Lie group under certain conditions).
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