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Ten papers published by Geometry & Topology Publications
Posted:
Oct 30, 2011 12:00 AM


Two papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 29032936 Knotted Legendrian surfaces with few Reeb chords by Georgios Dimitroglou Rizell URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p093.xhtml DOI: 10.2140/agt.2011.11.2903
(2) Algebraic & Geometric Topology 11 (2011) 29372939 Erratum to the article Twisted Alexander polynomials and surjectivity of a group homomorphism by Teruaki Kitano, Masaaki Suzuki and Masaaki Wada URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p0C2.xhtml DOI: 10.2140/agt.2011.11.2937
Eight papers have been published by Geometry & Topology
(3) Geometry & Topology 15 (2011) 18831925 Coarse differentiation and quasiisometries of a class of solvable Lie groups I by Irine Peng URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p046.xhtml DOI: 10.2140/gt.2011.15.1883
(4) Geometry & Topology 15 (2011) 19271981 Coarse differentiation and quasiisometries of a class of solvable Lie groups II by Irine Peng URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p047.xhtml DOI: 10.2140/gt.2011.15.1927
(5) Geometry & Topology 15 (2011) 19832015 On the moduli space of positive Ricci curvature metrics on homotopy spheres by David J Wraith URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p048.xhtml DOI: 10.2140/gt.2011.15.1983
(6) Geometry & Topology 15 (2011) 20172071 Infinitesimal projective rigidity under Dehn filling by Michael Heusener and Joan Porti URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p049.xhtml DOI: 10.2140/gt.2011.15.2017
(7) Geometry & Topology 15 (2011) 20732089 Veering triangulations admit strict angle structures by Craig D Hodgson, J Hyam Rubinstein, Henry Segerman and Stephan Tillmann URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p050.xhtml DOI: 10.2140/gt.2011.15.2073
(8) Geometry & Topology 15 (2011) 20912110 Symplectic embeddings of ellipsoids in dimension greater than four by Olguta Buse and Richard Hind URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p051.xhtml DOI: 10.2140/gt.2011.15.2091
(9) Geometry & Topology 15 (2011) 21112133 Hodge theory on nearly Kahler manifolds by Misha Verbitsky URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p052.xhtml DOI: 10.2140/gt.2011.15.2111
(10) Geometry & Topology 15 (2011) 21352180 Asymptotics of the colored Jones function of a knot by Stavros Garoufalidis and Thang T Q Le URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p053.xhtml DOI: 10.2140/gt.2011.15.2135
Abstracts follow
(1) Knotted Legendrian surfaces with few Reeb chords by Georgios Dimitroglou Rizell
For g>0, we construct g+1 Legendrian embeddings of a surface of genus g into J^1(R^2)=R^5 which lie in pairwise distinct Legendrian isotopy classes and which all have g+1 transverse Reeb chords (g+1 is the conjecturally minimal number of chords). Furthermore, for g of the g+1 embeddings the Legendrian contact homology DGA does not admit any augmentation over Z_2, and hence cannot be linearized. We also investigate these surfaces from the point of view of the theory of generating families. Finally, we consider Legendrian spheres and planes in J^1(S^2) from a similar perspective.
(2) Erratum to the article Twisted Alexander polynomials and surjectivity of a group homomorphism by Teruaki Kitano, Masaaki Suzuki and Masaaki Wada
We prove the nonexistence of surjective homomorphisms from knot groups G(8_{21}), G(9_{12}), G(9_{24}), G(9_{39}) onto G(4_1) using twisted Alexander polynomials and the numbers of surjective homomorphisms onto SL(2;Z/7Z).
(3) Coarse differentiation and quasiisometries of a class of solvable Lie groups I by Irine Peng
This is the first of two consecutive papers that aim to understand quasiisometries of a class of unimodular split solvable Lie groups. In the present paper, we show that locally (in a coarse sense), a quasiisometry between two groups in this class is close to a map that respects their group structures. In the following paper we will use this result to show quasiisometric rigidity.
(4) Coarse differentiation and quasiisometries of a class of solvable Lie groups II by Irine Peng
In this paper, we continue with the results of the preceeding paper and compute the group of quasiisometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasiisometric to a member of the subclass has to be polycyclic and is virtually a lattice in an abelianbyabelian solvable Lie group. We also give an example of a unimodular solvable Lie group that is not quasiisometric to any finitely generated group, as well deduce some quasiisometric rigidity results.
(5) On the moduli space of positive Ricci curvature metrics on homotopy spheres by David J Wraith We show that the moduli space of Ricci positive metrics on a certain family of homotopy spheres has infinitely many components.
(6) Infinitesimal projective rigidity under Dehn filling by Michael Heusener and Joan Porti
To a hyperbolic manifold one can associate a canonical projective structure and a fundamental question is whether or not it can be deformed. In particular, the canonical projective structure of a finite volume hyperbolic manifold with cusps might have deformations which are trivial on the cusps.
The aim of this article is to prove that if the canonical projective structure on a cusped hyperbolic manifold M is infinitesimally projectively rigid relative to the cusps, then infinitely many hyperbolic Dehn fillings on M are locally projectively rigid. We analyze in more detail the figure eight knot and the Whitehead link exteriors, for which we can give explicit infinite families of slopes with projectively rigid Dehn fillings.
(7) Veering triangulations admit strict angle structures by Craig D Hodgson, J Hyam Rubinstein, Henry Segerman and Stephan Tillmann
Agol recently introduced the concept of a veering taut triangulation of a 3manifold, which is a taut ideal triangulation with some extra combinatorial structure. We define the weaker notion of a "veering triangulation" and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, giving an example of a veering taut triangulation that is not layered.
(8) Symplectic embeddings of ellipsoids in dimension greater than four by Olguta Buse and Richard Hind
We study symplectic embeddings of ellipsoids into balls. In the main construction, we show that a given embedding of 2mdimensional ellipsoids can be suspended to embeddings of ellipsoids in any higher dimension. In dimension 6,s if the ratio of the areas of any two axes is sufficiently large then the ellipsoid is flexible in the sense that it fully fills a ball. We also show that the same property holds in all dimensions for sufficiently thin ellipsoids E(1,..., a). A consequence of our study is that in arbitrary dimension a ball can be fully filled by any sufficiently large number of identical smaller balls, thus generalizing a result of Biran valid in dimension 4.
(9) Hodge theory on nearly Kahler manifolds by Misha Verbitsky
Let (M,I,omega,Omega) be a nearly Kahler 6manifold, that is, an SU(3)manifold with (3,0)form Omega and Hermitian form omega which satisfies domega=3*lambda*Re(Omega), d Im(Omega)=2*lambda*omega^2, for a nonzero real constant lambda. We develop an analogue of the Kahler relations on M, proving several useful identities for various intrinsic Laplacians on M. When M is compact, these identities give powerful results about cohomology of M. We show that harmonic forms on M admit a Hodge decomposition, and prove that H^{p,q}(M)=0 unless p=q or (p=1,q=2) or (p=2,q=1).
(10) Asymptotics of the colored Jones function of a knot by Stavros Garoufalidis and Thang T Q Le
To a knot in 3space, one can associate a sequence of Laurent polynomials, whose nth term is the nth colored Jones polynomial. The paper is concerned with the asymptotic behavior of the value of the nth colored Jones polynomial at e^{a/n}, when a is a fixed complex number and n tends to infinity. We analyze this asymptotic behavior to all orders in 1/n when a is a sufficiently small complex number. In addition, we give upper bounds for the coefficients and degree of the nth colored Jones polynomial, with applications to upper bounds in the Generalized Volume Conjecture. Work of Agol, Dunfield, Storm and W Thurston implies that our bounds are asymptotically optimal. Moreover, we give results for the Generalized Volume Conjecture when a is near 2*pi*i. Our proofs use crucially the cyclotomic expansion of the colored Jones function, due to Habiro.
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