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Geometry and Topology

Posts: 139
Registered: 5/24/06
Ten papers published by Geometry & Topology Publications
Posted: Jul 27, 2011 1:30 PM
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Six papers have been published by Algebraic & Geometric Topology

(1) Algebraic & Geometric Topology 11 (2011) 1961-1985
Poincare duality and periodicity
by John R Klein and William Richter
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p064.xhtml
DOI: 10.2140/agt.2011.11.1961

(2) Algebraic & Geometric Topology 11 (2011) 1987-2005
Flipping bridge surfaces and bounds on the stable bridge number
by Jesse Johnson and Maggy Tomova
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p065.xhtml
DOI: 10.2140/agt.2011.11.1987

(3) Algebraic & Geometric Topology 11 (2011) 2007-2035
On the Chabauty space of locally compact abelian groups
by Yves Cornulier
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p066.xhtml
DOI: 10.2140/agt.2011.11.2007

(4) Algebraic & Geometric Topology 11 (2011) 2037-2106
Generic deformations of the colored sl(N)-homology for links
by Hao Wu
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p067.xhtml
DOI: 10.2140/agt.2011.11.2037

(5) Algebraic & Geometric Topology 11 (2011) 2107-2135
Rational Z_p-equivariant spectra
by David Barnes
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p068.xhtml
DOI: 10.2140/agt.2011.11.2107

(6) Algebraic & Geometric Topology 11 (2011) 2137-2166
SO(3) homology of graphs and links
by Benjamin Cooper, Matt Hogancamp and Vyacheslav Krushkal
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p069.xhtml
DOI: 10.2140/agt.2011.11.2137

Four papers have been published by Geometry & Topology. These
complete Volume 15 Issue 2

(7) Geometry & Topology 15 (2011) 1107-1124
On macroscopic dimension of rationally essential manifolds
by Alexander Dranishnikov
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p029.xhtml
DOI: 10.2140/gt.2011.15.1107

(8) Geometry & Topology 15 (2011) 1125-1156
On rational homology disk smoothings of valency 4 surface singularities
by Jonathan Wahl
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p030.xhtml
DOI: 10.2140/gt.2011.15.1125

(9) Geometry & Topology 15 (2011) 1157-1168
Cosmetic surgery in L-space homology spheres
by Zhongtao Wu
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p031.xhtml
DOI: 10.2140/gt.2011.15.1157

(10) Geometry & Topology 15 (2011) 1169-1224
Local topology in deformation spaces of hyperbolic 3-manifolds
by Jeffrey F Brock, Kenneth W Bromberg, Richard D Canary and Yair N Minsky
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p032.xhtml
DOI: 10.2140/gt.2011.15.1169

Abstracts follow

(1) Poincare duality and periodicity
by John R Klein and William Richter

We construct periodic families of Poincare complexes, partially
solving a question of Hodgson, and infinite families of Poincare
complexes whose top cell falls off after one suspension but which fail
to embed in a sphere of codimension one. We give a homotopy theoretic
description of the four-fold periodicity in knot cobordism.


(2) Flipping bridge surfaces and bounds on the stable bridge number
by Jesse Johnson and Maggy Tomova

We show that if K is a knot in the 3-sphere and Sigma is a bridge
sphere for K with high distance and 2n punctures, the number of
perturbations of K required to interchange the two balls bounded by
Sigma via an isotopy is n. We also construct a knot with two
different bridge spheres with 2n and 2n-1 bridges respectively for
which any common perturbation has at least 3n-4 bridges. We generalize
both of these results to bridge surfaces for knots in any 3-manifold.


(3) On the Chabauty space of locally compact abelian groups
by Yves Cornulier

This paper contains several results about the Chabauty space of a general
locally compact abelian group. Notably, we determine its topological
dimension, we characterize when it is totally disconnected or connected;
we characterize isolated points.


(4) Generic deformations of the colored sl(N)-homology for links
by Hao Wu

We generalize the works of Lee [Adv. Math. 197 (2005) 554--586] and
Gornik [arXiv math.QA/0402266] to construct a basis for generic
deformations of the colored sl(N)-homology defined in [arXiv
1002.2662v2]. As applications, we construct nondegenerate pairings and
co-pairings which lead to dualities of generic deformations of the
colored sl(N)-homology. We also define and study colored
sl(N)-Rasmussen invariants. Among other things, we observe that these
invariants vanish on amphicheiral knots and discuss some implications
of this observation.


(5) Rational Z_p-equivariant spectra
by David Barnes

We find a simple algebraic model for rational Z_p-equivariant spectra, via
a series of Quillen equivalences. This model, along with an Adams short exact
sequence, will allow us to easily perform constructions and calculations.


(6) SO(3) homology of graphs and links
by Benjamin Cooper, Matt Hogancamp and Vyacheslav Krushkal

The SO(3) Kauffman polynomial and the chromatic polynomial of planar
graphs are categorified by a unique extension of the Khovanov homology
framework. Many structural observations and computations of homologies
of knots and spin networks are included.


(7) On macroscopic dimension of rationally essential manifolds
by Alexander Dranishnikov

We construct a counterexamples in dimensions n>3 to Gromov's
conjecture that the macroscopic dimension of rationally essential
n-dimensional manifolds equals n.


(8) On rational homology disk smoothings of valency 4 surface singularities
by Jonathan Wahl

Thanks to recent work of Stipsicz, Szabo and the author and of Bhupal
and Stipsicz, one has a complete list of resolution graphs of weighted
homogeneous complex surface singularities admitting a rational
homology disk ("QHD") smoothing, that is, one with Milnor number 0.
They fall into several classes, the most interesting of which are the
3 classes whose resolution dual graph has central vertex with valency
4. We give a uniform "quotient construction" of the QHD smoothings
for those classes; it is an explicit Q-Gorenstein smoothing, yielding
a precise description of the Milnor fibre and its non-abelian
fundamental group. This had already been done for two of these
classes; what is new here is the construction of the third class,
which is far more difficult. In addition, we explain the existence of
two different QHD smoothings for the first class.

We also prove a general formula for the dimension of a QHD smoothing
component for a rational surface singularity. A corollary is that for
the valency 4 cases, such a component has dimension 1 and is smooth.
Another corollary is that "most" H-shaped resolution graphs cannot be
the graph of a singularity with a QHD smoothing. This result, plus
recent work of Bhupal and Stipsicz, is evidence for a general
conjecture:

Conjecture: The only complex surface singularities admitting a QHD
smoothing are the (known) weighted homogeneous examples.


(9) Cosmetic surgery in L-space homology spheres
by Zhongtao Wu

Let K be a nontrivial knot in the 3-sphere, and let r and r' be two
distinct rational numbers of same sign. We prove that there is no
orientation-preserving homeomorphism between the manifolds given by
Dehn surgery along K with slopes r and r'. We further generalize this
uniqueness result to knots in arbitrary L-space homology spheres.


(10) Local topology in deformation spaces of hyperbolic 3-manifolds
by Jeffrey F Brock, Kenneth W Bromberg, Richard D Canary and Yair N Minsky

We prove that the deformation space AH(M) of marked hyperbolic
3-manifolds homotopy equivalent to a fixed compact 3-manifold M with
incompressible boundary is locally connected at minimally parabolic
points. Moreover, spaces of Kleinian surface groups are locally
connected at quasiconformally rigid points. Similar results are
obtained for deformation spaces of acylindrical 3-manifolds and Bers
slices.



Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers




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