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Geometry and Topology

Posts: 140
Registered: 5/24/06
Eight papers published by Geometry & Topology Publications
Posted: May 22, 2012 12:11 PM
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Three papers have been published by Algebraic & Geometric Topology

(1) Algebraic & Geometric Topology 12 (2012) 1099-1136
Partial duals of plane graphs, separability and the graphs of knots
by Iain Moffatt
URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p040.xhtml
DOI: 10.2140/agt.2012.12.1099

(2) Algebraic & Geometric Topology 12 (2012) 1137-1143
Normalizers of parabolic subgroups of Coxeter groups
by Daniel Allcock
URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p041.xhtml
DOI: 10.2140/agt.2012.12.1137

(3) Algebraic & Geometric Topology 12 (2012) 1145-1163
On symplectic uniruling of Hamiltonian fibrations
by Clement Hyvrier
URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p042.xhtml
DOI: 10.2140/agt.2012.12.1145

Five papers have been published by Geometry & Topology

(4) Geometry & Topology 16 (2012) 781-888
Geometry and rigidity of mapping class groups
by Jason Behrstock, Bruce Kleiner, Yair Minsky and Lee Mosher
URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/p017.xhtml
DOI: 10.2140/gt.2012.16.781

(5) Geometry & Topology 16 (2012) 889-917
Milnor invariants and the HOMFLYPT Polynomial
by Jean-Baptiste Meilhan and Akira Yasuhara
URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/p018.xhtml
DOI: 10.2140/gt.2012.16.889

(6) Geometry & Topology 16 (2012) 919-955
Long knots and maps between operads
by William Dwyer and Kathryn Hess
URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/p019.xhtml
DOI: 10.2140/gt.2012.16.919

(7) Geometry & Topology 16 (2012) 957-962
Rigidity for odd-dimensional souls
by Kristopher Tapp
URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/p020.xhtml
DOI: 10.2140/gt.2012.16.957

(8) Geometry & Topology 16 (2012) 963-1052
Lagrangian topology and enumerative geometry
by Paul Biran and Octav Cornea
URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/p021.xhtml
DOI: 10.2140/gt.2012.16.963

Abstracts follow

(1) Partial duals of plane graphs, separability and the graphs of knots
by Iain Moffatt

There is a well-known way to describe a link diagram as a (signed)
plane graph, called its Tait graph. This concept was recently
extended, providing a way to associate a set of embedded graphs (or
ribbon graphs) to a link diagram. While every plane graph arises as a
Tait graph of a unique link diagram, not every embedded graph
represents a link diagram. Furthermore, although a Tait graph
describes a unique link diagram, the same embedded graph can represent
many different link diagrams. One is then led to ask which embedded
graphs represent link diagrams, and how link diagrams presented by the
same embedded graphs are related to one another. Here we answer these
questions by characterizing the class of embedded graphs that
represent link diagrams, and then using this characterization to find
a move that relates all of the link diagrams that are presented by the
same set of embedded graphs.


(2) Normalizers of parabolic subgroups of Coxeter groups
by Daniel Allcock

We improve a bound of Borcherds on the virtual cohomological dimension
of the nonreflection part of the normalizer of a parabolic subgroup of
a Coxeter group. Our bound is in terms of the types of the components
of the corresponding Coxeter subdiagram rather than the number of
nodes. A consequence is an extension of Brink's result that the
nonreflection part of a reflection centralizer is free. Namely, the
nonreflection part of the normalizer of parabolic subgroup of type D_5
or A_m for m odd, is either free or has a free subgroup of index 2.


(3) On symplectic uniruling of Hamiltonian fibrations
by Clement Hyvrier

Under certain conditions of technical order, we show that closed
connected Hamiltonian fibrations over symplectically uniruled
manifolds are also symplectically uniruled. As a consequence, we
partially extend to nontrivial Hamiltonian fibrations a result of Lu
[Math. Res. Lett. 7 (2000) 383--387], stating that any trivial
symplectic product of two closed symplectic manifolds with one of them
being symplectically uniruled verifies the Weinstein Conjecture for
closed separating hypersurfaces of contact type. The proof of our
result is based on the product formula for Gromov--Witten invariants
of Hamiltonian fibrations derived by the author in [arXiv 0904.1492].


(4) Geometry and rigidity of mapping class groups
by Jason Behrstock, Bruce Kleiner, Yair Minsky and Lee Mosher

We study the large scale geometry of mapping class groups MCG(S),
using hyperbolicity properties of curve complexes. We show that any
self quasi-isometry of MCG(S) (outside a few sporadic cases) is a
bounded distance away from a left-multiplication, and as a consequence
obtain quasi-isometric rigidity for MCG(S), namely that groups
quasi-isometric to MCG(S) are equivalent to it up to extraction of
finite-index subgroups and quotients with finite kernel. (The latter
theorem was proved by Hamenstadt using different methods).

As part of our approach we obtain several other structural results: a
description of the tree-graded structure on the asymptotic cone of
MCG(S); a characterization of the image of the curve complex
projections map from MCG(S) to the product of C(Y) over all Y in S;
and a construction of Sigma-hulls in MCG(S), an analogue of convex
hulls.


(5) Milnor invariants and the HOMFLYPT Polynomial
by Jean-Baptiste Meilhan and Akira Yasuhara

We give formulas expressing Milnor invariants of an n-component link L
in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If
the Milnor invariant mu-bar_L(J) vanishes for any sequence J with
length at most k, then any Milnor mu-bar-invariant mu-bar_L(I) with
length between 3 and 2k+1 can be represented as a combination of
HOMFLYPT polynomial of knots obtained from the link by certain band
sum operations. In particular, the "first nonvanishing" Milnor
invariants can be always represented as such a linear combination.


(6) Long knots and maps between operads
by William Dwyer and Kathryn Hess

We identify the space of tangentially straightened long knots in R^m,
m at least 4, as the double loops on the space of derived operad maps
from the associative operad into a version of the little m-disk
operad. This verifies a conjecture of Kontsevich, Lambrechts and
Turchin.


(7) Rigidity for odd-dimensional souls
by Kristopher Tapp

We prove a new rigidity result for an open manifold M with nonnegative
sectional curvature whose soul Sigma in M is odd-dimensional.
Specifically, there exists a geodesic in Sigma and a parallel vertical
plane field along it with constant vertical curvature and vanishing
normal curvature. Under the added assumption that the Sharafutdinov
fibers are rotationally symmetric, this implies that for small r, the
distance sphere B_r(Sigma)={p in M | dist(p,Sigma)=r} contains an
immersed flat cylinder, and thus could not have positive curvature.


(8) Lagrangian topology and enumerative geometry
by Paul Biran and Octav Cornea

We analyze the properties of Lagrangian quantum homology (in the form
constructed in our previous work, based on the pearl complex) to
associate certain enumerative invariants to monotone Lagrangian
submanifolds. The most interesting such invariant is given as the
discriminant of a certain quadratic form. For 2-dimensional
Lagrangians it corresponds geometrically to counting certain types of
configurations involving pseudoholomorphic disks that are associated
to triangles on the respective surface. We analyze various properties
of these invariants and compute them and the related structures for a
wide class of toric fibers. An appendix contains an explicit
description of the orientation conventions and verifications required
to establish quantum homology and the related structures over the
integers.



Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers



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