Subject: new Hopf listings
Date: 02 Jan 2002 09:32:58 -0500
From: Mark Hovey
To: dmd1@lehigh.edu
Happy New Year! 4 new papers this time, from Bendersky-Hunton, Chorny
(2), and Hunton-Schuster.
Mark Hovey
New papers appearing on hopf between 12/12/01 and 01/02/02
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bendersky-Hunton/BH2
On the coalgebraic ring and Bousfield-Kan spectral sequence
for a Landweber exact spectrum
Martin Bendersky and John R. Hunton
We construct a Bousfield-Kan (unstable Adams) spectral sequence
based on an arbitrary (and not necessarily connective) ring
spectrum $E$ with unit and which is related to the homotopy groups
of a certain unstable $E$ completion $\xe$ of a space $X$. For $E$
an S-Algebra this completion agrees with that of the first author
and R. Thompson. We also establish in detail the Hopf algebra
structure of the unstable cooperations (the coalgebraic module)
$E_*(\EE_*)$ for an arbitrary Landweber exact spectrum $E$,
extending work of the second author and M. Hopkins\cite and giving
basis-free descriptions of the modules of primitives and
indecomposables. Taken together, these results enable us to give a
simple description of the $E_2$-term of the $E$-theory
Bousfield-Kan spectral sequence when $E$ is any Landweber exact
ring spectrum with unit. This extends work of the first author and
others and gives a tractable unstable Adams spectral sequence
based on a $v_n$-periodic theory for all~$n$.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/ChornyB/diag
An example of a non-cofibrantly generated model category
Boris Chorny
AMS Classification numbers
Primary 55U35; Secondary 55P91, 18G55
Centre de Recerca Matematica, Apartat 50, E-08193 Bellaterra
(Barcelona), Spain
cboris@crm.es
We show that the model category of diagrams of spaces generated by a
proper class of orbits is not cofibrantly generated. In particular the
category of maps between spaces may be given a non-cofibrantly generated
model structure.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/ChornyB/ehomology
Equivariant cellular homology and its applications
Boris Chorny
AMS Classification numbers
Primary 55N91; Secondary 55P91, 57S99
Einstein Institute of Mathematics, Edmond Safra Campus,
Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
chorny@math.huji.ac.il
In this work we develop a cellular equivariant homology
functor and apply it to prove an equivariant Euler-Poincare formula and
an equivariant Lefschetz theorem.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Hunton-Schuster/subalg
Title: Subalgebras of group cohomology defined by infinite loop spaces
Authors: John R. Hunton
Bj"orn Schuster
MSC: 20J06 55N20 55P47 (primary), 55R40 19A22 55P60 (secondary)
arXiv: math.AT/0112169
Addresses: The Department of Mathematics and Computer Science, University of
Leicester, University Road, Leicester, LE1 7RH, England
Department of Mathematics, University of Wuppertal, Gaussstr.~20,
D-42097 Wuppertal, Germany.
Abstract:
We study natural subalgebras Ch_E(G) of group cohomology defined in terms
of infinite loop spaces E and give representation theoretic descriptions of
those based on QS^0 and the Johnson-Wilson theories E(n). We describe the
subalgebras arising from the Brown-Peterson spectra BP and as a result give
a simple reproof of Yagita's theorem that the image of BP^*(BG) in
H^*(BG;F_p) is F-isomorphic to the whole cohomology ring; the same result
is shown to hold with BP replaced by any complex oriented theory E with a
map of ring spectra from E to HF_p which is non-trivial in homotopy. We
also extend the constructions to define subalgebras of H^*(X;F_p) for any
space X; when X is finite we show that the subalgebras Ch_{E(n)}(X)
give a natural unstable chromatic filtration of H^*(X;F_p).
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