Subject: new Hopf listings
From: Mark Hovey
Date: 14 May 2007 09:05:17 -0400
4 new papers this month, from Barge-Lannes, Biedermann, Bubenik, and
Devinatz.
Mark Hovey
New papers appearing on hopf between 4/19/07 and 5/14/07
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Barge-Lannes/SMB
Title: Suites de Sturm, indice de Maslov et p\'e riodicit\'e de Bott
Authors: Jean Barge and Jean Lannes
Abstract: This memoir presents a reworking of a very classical subject; it
is related to works of many people, especially: Richard W. Sharpe, Max
Karoubi, Andrew Ranicki, Fran\c{c}ois Latour... We explain in particular
how the usual theory of Sturm sequences is linked to the fundamental
theorem of hermitian K-theory (due to Karoubi) and to Bott periodicity.
Keywords: Sturm sequences, Maslov index, Bott periodicity, hermitian
K-theory.
AMS classification: 19G38, 19C99.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Biedermann/L-stable
L-stable functors
by Georg Biedermann
We generalize and greatly simplify the approach of Lydakis and
Dundas-R\"ondigs-{\O}stv{\ae}r to construct an L-stable model structure
for small functors from a closed symmetric monoidal model category V to
a V-model category M, where L is a small cofibrant object of V. For the
special case V=M=S_* pointed simplicial sets and L=S1 this is the
classical case of linear functors and has been described as the first
stage of the Goodwillie tower of a homotopy functor. We show, that our
various model structures are compatible with a closed symmetric monoidal
product on small functors. We compare them with other L-stabilizations
described by Hovey, Jardine and others. This gives a particularly easy
construction of the classical and the motivic stable homotopy category
with the correct smash product. We establish the monoid axiom under
certain conditions.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bubenik/sep
Author: Peter Bubenik
Title: Separated Lie models and the homotopy Lie algebra
AMS classification number: Primary 55P62; Secondary 17B55
to appear in the Journal of Pure and Applied Algebra
Abstract:
The homotopy Lie algebra of a simply connected topological space, X, is
given by the rational homotopy groups on the loop space of X. Following
Quillen, there is a connected differential graded free Lie algebra (dgL)
called a Lie model, which determines the rational homotopy type of X,
and whose homology is isomorphic to the homotopy Lie algebra. We show
that such a Lie model can be replaced with one that has a special
property we call separated. The homology of a separated dgL has a
particular form which lends itself to calculations. We give connections
to the radical of the homotopy Lie algebra and the Avramov-Felix
conjecture. Examples that are worked out in detail include wedges of
spheres on any "thickness" and connected sums of products of spheres.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Devinatz/towardsfiniteness
Title: Towards the finiteness of the homotopy groups of the
K(n)-localization
of S0.
Author: Ethan S. Devinatz
Abstract: Let G be a closed subgroup of the nth Morava stabilizer group
S_n, n>1, and let E_n^{hG} denote the continuous homotopy fixed point
spectrum of Devinatz and Hopkins. If G=, the subgroup topologically
generated by an element z in the p-Sylow subgroup S_n0 of S_n, and z is
non-torsion in the quotient of S_n0 by its center, we prove that the
E_n^{h}-homology of any K(n-2)-acyclic finite spectrum annihilated by
p is of essentially finite rank. (The definition of essentially finite
rank is given in the paper.) We also show that the units in the
coefficient ring of E_n which are fixed by z are just the units in the
Witt vectors with coefficients in the field of p^n elements. If n=2 and
p>3, we show that, if G is a closed subgroup of S_n0 not contained in
the center, then G contains an open subnormal subgroup U such that the
mod(p) homotopy of E_n^{hV} is of essentially finite rank, where V is
the product of U with the units in the field of p elements.
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