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Eleven papers published by Geometry & Topology Publications
Posted:
May 24, 2011 10:00 AM
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Eight papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 1323-1343
The moduli space of hex spheres
by Aldo-Hilario Cruz-Cota
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p042.xhtml
DOI: 10.2140/agt.2011.11.1323
(2) Algebraic & Geometric Topology 11 (2011) 1345-1359
Nonsmoothable group actions on spin 4-manifolds
by Kazuhiko Kiyono
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p043.xhtml
DOI: 10.2140/agt.2011.11.1345
(3) Algebraic & Geometric Topology 11 (2011) 1361-1403
Units of equivariant ring spectra
by Rekha Santhanam
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p044.xhtml
DOI: 10.2140/agt.2011.11.1361
(4) Algebraic & Geometric Topology 11 (2011) 1405-1433
Complete graphs whose topological symmetry groups are polyhedral
by Erica Flapan, Blake Mellor and Ramin Naimi
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p045.xhtml
DOI: 10.2140/agt.2011.11.1405
(5) Algebraic & Geometric Topology 11 (2011) 1435-1443
Dividing sets as nodal sets of an eigenfunction of the Laplacian
by Samuel T Lisi
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p046.xhtml
DOI: 10.2140/agt.2011.11.1435
(6) Algebraic & Geometric Topology 11 (2011) 1445-1454
On links with locally infinite Kakimizu complexes
by Jessica E Banks
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p047.xhtml
DOI: 10.2140/agt.2011.11.1445
(7) Algebraic & Geometric Topology 11 (2011) 1455-1469
Systoles of hyperbolic manifolds
by Mikhail V Belolipetsky and Scott A Thomson
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p048.xhtml
DOI: 10.2140/agt.2011.11.1455
(8) Algebraic & Geometric Topology 11 (2011) 1471-1495
Complexes and exactness of certain Artin groups
by Erik Guentner and Graham A Niblo
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p049.xhtml
DOI: 10.2140/agt.2011.11.1471
Three papers have been published by Geometry & Topology
(9) Geometry & Topology 15 (2011) 707-733
Orthospectra of geodesic laminations and dilogarithm identities on moduli space
by Martin Bridgeman
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p020.xhtml
DOI: 10.2140/gt.2011.15.707
(10) Geometry & Topology 15 (2011) 735-764
Concerning the existence of Einstein and Ricci soliton metrics on solvable Lie groups
by Michael Jablonski
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p021.xhtml
DOI: 10.2140/gt.2011.15.735
(11) Geometry & Topology 15 (2011) 765-826
Target-local Gromov compactness
by Joel W Fish
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p022.xhtml
DOI: 10.2140/gt.2011.15.765
Abstracts follow
(1) The moduli space of hex spheres
by Aldo-Hilario Cruz-Cota
A hex sphere is a singular Euclidean sphere with four cone points whose
cone angles are (integer) multiples of 2pi/3 but less than 2pi. We prove
that the Moduli space of hex spheres of unit area is homeomorphic to
the the space of similarity classes of Voronoi polygons in the Euclidean
plane. This result gives us as a corollary that each unit-area hex sphere
M satisfies the following properties:
(1) it has an embedded (open Euclidean) annulus that is disjoint from the
singular locus of M;
(2) it embeds isometrically in the 3-dimensional Euclidean space as the
boundary of a tetrahedron; and
(3) there is a simple closed geodesic gamma in M such that a fractional
Dehn twist along gamma converts M to the double of a parallelogram.
(2) Nonsmoothable group actions on spin 4-manifolds
by Kazuhiko Kiyono
We show that every closed, simply connected, spin topological
4-manifold except the 4-sphere and the product of the 2-sphere with
itself admits a homologically trivial, pseudofree, locally linear
action of cyclic group of any sufficiently large prime order which is
nonsmoothable for any possible smooth structure.
(3) Units of equivariant ring spectra
by Rekha Santhanam
It is well known that very special Gamma-spaces and grouplike
E_infinity-spaces both model connective spectra. Both these models
have equivariant analogues in the case when the group acting is
finite. Shimakawa defined the category of equivariant Gamma-spaces
and showed that special equivariant Gamma-spaces determine positive
equivariant spectra. Costenoble and Waner [Trans. Amer. Math. Soc. 326
(1991) 485-505] showed that grouplike equivariant E_infinity-spaces
determine connective equivariant spectra.
We show that with suitable model category structures the category of
equivariant Gamma-spaces is Quillen equivalent to the category of
equivariant E_infinity-spaces. We define the units of equivariant ring
spectra in terms of equivariant Gamma-spaces and show that the units
of an equivariant ring spectrum determines a connective equivariant
spectrum.
(4) Complete graphs whose topological symmetry groups are polyhedral
by Erica Flapan, Blake Mellor and Ramin Naimi
We determine for which m the complete graph K_m has an embedding in
the three-sphere whose topological symmetry group is isomorphic to one
of the polyhedral groups A_4, A_5 or S_4.
(5) Dividing sets as nodal sets of an eigenfunction of the Laplacian
by Samuel T Lisi
We show that for any convex surface S in a contact 3-manifold, there
exists a metric on S and a neighbourhood contact isotopic to S times I
with the contact structure given by ker(u dt - star du) where u is an
eigenfunction of the Laplacian on S and star is the Hodge star from
the metric on S. This answers a question posed by Komendarczyk
[Trans. Amer. Math. Soc. 358 (2006) 2399--2413].
(6) On links with locally infinite Kakimizu complexes
by Jessica E Banks
We show that the Kakimizu complex of a knot may be locally infinite,
answering a question of Przytycki-Schultens. We then prove that if a
link L only has connected Seifert surfaces and has a locally infinite
Kakimizu complex then L is a satellite of either a torus knot, a cable
knot or a connected sum, with winding number 0.
(7) Systoles of hyperbolic manifolds
by Mikhail V Belolipetsky and Scott A Thomson
We show that for every n>=2 and any epsilon > 0 there exists a
compact hyperbolic n-manifold with a closed geodesic of length less
than epsilon. When epsilon is sufficiently small these manifolds are
non-arithmetic, and they are obtained by a generalised inbreeding
construction which was first suggested by Agol for n = 4. We also
show that for n >= 3 the volumes of these manifolds grow at least as
1/epsilon^{n-2} when epsilon --> 0.
(8) Complexes and exactness of certain Artin groups
by Erik Guentner and Graham A Niblo
In his work on the Novikov conjecture, Yu introduced Property A as a
readily verified criterion implying coarse embeddability. Studied
subsequently as a property in its own right, Property A for a discrete
group is known to be equivalent to exactness of the reduced group
C^*-algebra and to the amenability of the action of the group on its
Stone--Cech compactification. In this paper we study exactness for
groups acting on a finite dimensional CAT(0) cube complex. We apply
our methods to show that Artin groups of type FC are exact. While
many discrete groups are known to be exact the question of whether
every Artin group is exact remains open.
(9) Orthospectra of geodesic laminations and dilogarithm identities on moduli space
by Martin Bridgeman
Given a measured lamination lambda on a finite area hyperbolic surface
we consider a natural measure M_lambda on the real line obtained
by taking the push-forward of the volume measure of the unit tangent
bundle of the surface under an intersection function associated with the
lamination. We show that the measure M_lambda gives summation identities
for the Rogers dilogarithm function on the moduli space of a surface.
(10) Concerning the existence of Einstein and Ricci soliton metrics on solvable Lie groups
by Michael Jablonski
In this work we investigate solvable and nilpotent Lie groups with
special metrics. The metrics of interest are left-invariant Einstein
and algebraic Ricci soliton metrics. Our main result shows that one
may determine the existence of a such a metric by analyzing algebraic
properties of the Lie algebra and infinitesimal deformations of any
initial metric.
Our second main result concerns the isometry groups of such
distinguished metrics. Among the completely solvable unimodular Lie
groups (this includes nilpotent groups), if the Lie group admits such
a metric, we show that the isometry group of this special metric is
maximal among all isometry groups of left-invariant metrics.
(11) Target-local Gromov compactness
by Joel W Fish
We prove a version of Gromov's compactness theorem for pseudoholomorphic
curves which holds locally in the target symplectic manifold. This result
applies to sequences of curves with an unbounded number of free boundary
components, and in families of degenerating target manifolds which have
unbounded geometry (eg no uniform energy threshold). Core elements of the
proof regard curves as submanifolds (rather than maps) and then adapt methods
from the theory of minimal surfaces.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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