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Geometry and Topology

Posts: 139
Registered: 5/24/06
Eight papers published by Geometry & Topology Publications
Posted: Jan 19, 2012 2:00 PM
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We have started publication in 2012 with papers (1) to (3) opening
AGT Volume 12 and papers (4) to (8) opening GT Volume 16.

Three papers have been published by Algebraic & Geometric Topology

(1) Algebraic & Geometric Topology 12 (2012) 1-18
Statistical hyperbolicity in groups
by Moon Duchin, Samuel Lelievre and Christopher Mooney
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p001.xhtml
DOI: 10.2140/agt.2012.12.1

(2) Algebraic & Geometric Topology 12 (2012) 19-35
A lower bound for the number of group actions on a compact Riemann surface
by James W Anderson and Aaron Wootton
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p002.xhtml
DOI: 10.2140/agt.2012.12.19

(3) Algebraic & Geometric Topology 12 (2012) 37-47
Expanders and property A
by Ana Khukhro and Nick J Wright
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p003.xhtml
DOI: 10.2140/agt.2012.12.37

Five papers have been published by Geometry & Topology

(4) Geometry & Topology 16 (2012) 1-110
Ideal boundaries of pseudo-Anosov flows and uniform convergence
groups with connections and applications to large scale geometry
by Sergio Fenley
URL: http://www.msp.warwick.ac.uk/gt/2012/16-01/p001.xhtml
DOI: 10.2140/gt.2012.16.1

(5) Geometry & Topology 16 (2012) 111-125
Small generating sets for the Torelli group
by Andrew Putman
URL: http://www.msp.warwick.ac.uk/gt/2012/16-01/p002.xhtml
DOI: 10.2140/gt.2012.16.111

(6) Geometry & Topology 16 (2012) 127-154
Quilted Floer trajectories with constant components:
Corrigendum to the article ``Quilted Floer cohomology''
by Katrin Wehrheim and Chris T Woodward
URL: http://www.msp.warwick.ac.uk/gt/2012/16-01/p0C1.xhtml
DOI: 10.2140/gt.2012.16.127

(7) Geometry & Topology 16 (2012) 155-217
Generalized Monodromy Conjecture in dimension two
by Andres Nemethi and Willem Veys
URL: http://www.msp.warwick.ac.uk/gt/2012/16-01/p004.xhtml
DOI: 10.2140/gt.2012.16.155

(8) Geometry & Topology 16 (2012) 219-299
Krull dimension for limit groups
by Larsen Louder
URL: http://www.msp.warwick.ac.uk/gt/2012/16-01/p005.xhtml
DOI: 10.2140/gt.2012.16.219

Abstracts follow

(1) Statistical hyperbolicity in groups
by Moon Duchin, Samuel Lelievre and Christopher Mooney

In this paper, we introduce a geometric statistic called the `sprawl'
of a group with respect to a generating set, based on the average
distance in the word metric between pairs of words of equal length.
The sprawl quantifies a certain obstruction to hyperbolicity. Group
presentations with maximum sprawl (ie without this obstruction) are
called `statistically hyperbolic'. We first relate sprawl to
curvature and show that nonelementary hyperbolic groups are
statistically hyperbolic, then give some results for products and for
certain solvable groups. In free abelian groups, the word metrics are
asymptotic to norms induced by convex polytopes, causing several kinds
of group invariants to reduce to problems in convex geometry. We
present some calculations and conjectures concerning the values taken
by the sprawl statistic for the group Z^d as the generators vary, by
studying the space R^d with various norms.


(2) A lower bound for the number of group actions on a compact Riemann surface
by James W Anderson and Aaron Wootton

We prove that the number of distinct group actions on compact Riemann
surfaces of a fixed genus sigma >= 2 is at least quadratic in sigma.
We do this through the introduction of a coarse signature space, the
space K_sigma of "skeletal signatures" of group actions on compact
Riemann surfaces of genus sigma. We discuss the basic properties of
K_sigma and present a full conjectural description.


(3) Expanders and property A
by Ana Khukhro and Nick J Wright

We give a cohomological characterisation of expander graphs, and use it to give
a direct proof that expander graphs do not have Yu's property A.


(4) Ideal boundaries of pseudo-Anosov flows and uniform convergence
groups with connections and applications to large scale geometry
by Sergio Fenley

Given a general pseudo-Anosov flow in a closed three manifold, the
orbit space of the lifted flow to the universal cover is homeomorphic
to an open disk. We construct a natural compactification of this orbit
space with an ideal circle boundary. If there are no perfect fits
between stable and unstable leaves and the flow is not topologically
conjugate to a suspension Anosov flow, we then show: The ideal circle
of the orbit space has a natural quotient space which is a
sphere. This sphere is a dynamical systems ideal boundary for a
compactification of the universal cover of the manifold. The main
result is that the fundamental group acts on the flow ideal boundary
as a uniform convergence group. Using a theorem of Bowditch, this
yields a proof that the fundamental group of the manifold is Gromov
hyperbolic and it shows that the action of the fundamental group on
the flow ideal boundary is conjugate to the action on the Gromov ideal
boundary. This gives an entirely new proof that the fundamental group
of a closed, atoroidal $3$--manifold which fibers over the circle is
Gromov hyperbolic. In addition with further geometric analysis, the
main result also implies that pseudo-Anosov flows without perfect fits
are quasigeodesic flows and that the stable/unstable foliations of
these flows are quasi-isometric foliations. Finally we apply these
results to (nonsingular) foliations: if a foliation is R-covered or
with one sided branching in an aspherical, atoroidal three manifold
then the results above imply that the leaves of the foliation in the
universal cover extend continuously to the sphere at infinity.


(5) Small generating sets for the Torelli group
by Andrew Putman

Proving a conjecture of Dennis Johnson, we show that the Torelli
subgroup I_g of the genus g mapping class group has a finite
generating set whose size grows cubically with respect to g. Our main
tool is a new space called the handle graph on which I_g acts
cocompactly.


(6) Quilted Floer trajectories with constant components:
Corrigendum to the article ``Quilted Floer cohomology''
by Katrin Wehrheim and Chris T Woodward

We fill a gap in the proof of the transversality result for quilted
Floer trajectories in [Geom. Topol. 14 (2010) 833--902] by addressing
trajectories for which some but not all components are constant.
Namely we show that for generic sets of split Hamiltonian
perturbations and split almost complex structures, the moduli spaces
of parametrized quilted Floer trajectories of a given index are smooth
of expected dimension. An additional benefit of the generic split
Hamiltonian perturbations is that they perturb the given cyclic
Lagrangian correspondence such that any geometric composition of its
factors is transverse and hence immersed.


(7) Generalized Monodromy Conjecture in dimension two
by Andres Nemethi and Willem Veys

The aim of the article is an extension of the Monodromy Conjecture of
Denef and Loeser in dimension two, incorporating zeta functions with
differential forms and targeting *all* monodromy eigenvalues, and also
considering singular ambient spaces. That is, we treat in a conceptual
unity the poles of the (generalized) topological zeta function and the
monodromy eigenvalues associated with an analytic germ f:(X,0)->(C,0)
defined on a normal surface singularity (X,0). The article targets
the "right" extension in the case when the link of (X,0) is a homology
sphere. As a first step, we prove a splice decomposition formula for
the topological zeta function Z(f,omega;s) for any f and analytic
differential form omega, which will play the key technical
localization tool in the later definitions and proofs.

Then, we define a set of "allowed" differential forms via a local
restriction along each splice component. For plane curves we show the
following three guiding properties:
(1) if s_0 is any pole of Z(f,omega;s) with omega allowed, then
exp(2*pi*i*s_0) is a monodromy eigenvalue of f, (2) the "standard"
form is allowed, (3) every monodromy eigenvalue of f is obtained as in
(1) for some allowed omega and some s_0.

For general (X,0) we prove (1) unconditionally, and (2)--(3) under an
additional (necessary) assumption, which generalizes the semigroup
condition of Neumann--Wahl. Several examples illustrate the
definitions and support the basic assumptions.


(8) Krull dimension for limit groups
by Larsen Louder

We show that varieties defined over free groups have finite Krull
dimension, answering a question of Z Sela.



Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers




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