4,042 research outputs found
Homology stability for outer automorphism groups of free groups
We prove that the quotient map from Aut(F_n) to Out(F_n) induces an
isomorphism on homology in dimension i for n at least 2i+4. This corrects an
earlier proof by the first author and significantly improves the stability
range. In the course of the proof, we also prove homology stability for a
sequence of groups which are natural analogs of mapping class groups of
surfaces with punctures. In particular, this leads to a slight improvement on
the known stability range for Aut(F_n), showing that its i-th homology is
independent of n for n at least 2i+2.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-54.abs.htm
Unimodular measures on the space of all Riemannian manifolds
We study unimodular measures on the space of all pointed
Riemannian -manifolds. Examples can be constructed from finite volume
manifolds, from measured foliations with Riemannian leaves, and from invariant
random subgroups of Lie groups. Unimodularity is preserved under weak* limits,
and under certain geometric constraints (e.g. bounded geometry) unimodular
measures can be used to compactify sets of finite volume manifolds. One can
then understand the geometry of manifolds with large, finite volume by
passing to unimodular limits.
We develop a structure theory for unimodular measures on ,
characterizing them via invariance under a certain geodesic flow, and showing
that they correspond to transverse measures on a foliated `desingularization'
of . We also give a geometric proof of a compactness theorem for
unimodular measures on the space of pointed manifolds with pinched negative
curvature, and characterize unimodular measures supported on hyperbolic
-manifolds with finitely generated fundamental group.Comment: 81 page
Testing the relevance of effective interaction potentials between highly charged colloids in suspension
Combining cell and Jellium model mean-field approaches, Monte Carlo together
with integral equation techniques, and finally more demanding many-colloid
mean-field computations, we investigate the thermodynamic behavior, pressure
and compressibility of highly charged colloidal dispersions, and at a more
microscopic level, the force distribution acting on the colloids. The
Kirkwood-Buff identity provides a useful probe to challenge the
self-consistency of an approximate effective screened Coulomb (Yukawa)
potential between colloids. Two effective parameter models are put to the test:
cell against renormalized Jellium models
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