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Eight papers published by Geometry & Topology Publications
Posted:
May 22, 2012 12:11 PM


Three papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 12 (2012) 10991136 Partial duals of plane graphs, separability and the graphs of knots by Iain Moffatt URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p040.xhtml DOI: 10.2140/agt.2012.12.1099
(2) Algebraic & Geometric Topology 12 (2012) 11371143 Normalizers of parabolic subgroups of Coxeter groups by Daniel Allcock URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p041.xhtml DOI: 10.2140/agt.2012.12.1137
(3) Algebraic & Geometric Topology 12 (2012) 11451163 On symplectic uniruling of Hamiltonian fibrations by Clement Hyvrier URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p042.xhtml DOI: 10.2140/agt.2012.12.1145
Five papers have been published by Geometry & Topology
(4) Geometry & Topology 16 (2012) 781888 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/2012/1602/p017.xhtml DOI: 10.2140/gt.2012.16.781
(5) Geometry & Topology 16 (2012) 889917 Milnor invariants and the HOMFLYPT Polynomial by JeanBaptiste Meilhan and Akira Yasuhara URL: http://www.msp.warwick.ac.uk/gt/2012/1602/p018.xhtml DOI: 10.2140/gt.2012.16.889
(6) Geometry & Topology 16 (2012) 919955 Long knots and maps between operads by William Dwyer and Kathryn Hess URL: http://www.msp.warwick.ac.uk/gt/2012/1602/p019.xhtml DOI: 10.2140/gt.2012.16.919
(7) Geometry & Topology 16 (2012) 957962 Rigidity for odddimensional souls by Kristopher Tapp URL: http://www.msp.warwick.ac.uk/gt/2012/1602/p020.xhtml DOI: 10.2140/gt.2012.16.957
(8) Geometry & Topology 16 (2012) 9631052 Lagrangian topology and enumerative geometry by Paul Biran and Octav Cornea URL: http://www.msp.warwick.ac.uk/gt/2012/1602/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 wellknown 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) 383387], 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 GromovWitten 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 quasiisometry of MCG(S) (outside a few sporadic cases) is a bounded distance away from a leftmultiplication, and as a consequence obtain quasiisometric rigidity for MCG(S), namely that groups quasiisometric to MCG(S) are equivalent to it up to extraction of finiteindex 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 treegraded 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 Sigmahulls in MCG(S), an analogue of convex hulls.
(5) Milnor invariants and the HOMFLYPT Polynomial by JeanBaptiste Meilhan and Akira Yasuhara
We give formulas expressing Milnor invariants of an ncomponent link L in the 3sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant mubar_L(J) vanishes for any sequence J with length at most k, then any Milnor mubarinvariant mubar_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 mdisk operad. This verifies a conjecture of Kontsevich, Lambrechts and Turchin.
(7) Rigidity for odddimensional 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 odddimensional. 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 2dimensional 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



