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Ten papers published by Geometry & Topology Publications
Posted:
Oct 30, 2011 12:00 AM
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Two papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 2903-2936
Knotted Legendrian surfaces with few Reeb chords
by Georgios Dimitroglou Rizell
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p093.xhtml
DOI: 10.2140/agt.2011.11.2903
(2) Algebraic & Geometric Topology 11 (2011) 2937-2939
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/2011/11-05/p0C2.xhtml
DOI: 10.2140/agt.2011.11.2937
Eight papers have been published by Geometry & Topology
(3) Geometry & Topology 15 (2011) 1883-1925
Coarse differentiation and quasi-isometries of a class of solvable Lie groups I
by Irine Peng
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p046.xhtml
DOI: 10.2140/gt.2011.15.1883
(4) Geometry & Topology 15 (2011) 1927-1981
Coarse differentiation and quasi-isometries of a class of solvable Lie groups II
by Irine Peng
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p047.xhtml
DOI: 10.2140/gt.2011.15.1927
(5) Geometry & Topology 15 (2011) 1983-2015
On the moduli space of positive Ricci curvature metrics on homotopy spheres
by David J Wraith
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p048.xhtml
DOI: 10.2140/gt.2011.15.1983
(6) Geometry & Topology 15 (2011) 2017-2071
Infinitesimal projective rigidity under Dehn filling
by Michael Heusener and Joan Porti
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p049.xhtml
DOI: 10.2140/gt.2011.15.2017
(7) Geometry & Topology 15 (2011) 2073-2089
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/2011/15-04/p050.xhtml
DOI: 10.2140/gt.2011.15.2073
(8) Geometry & Topology 15 (2011) 2091-2110
Symplectic embeddings of ellipsoids in dimension greater than four
by Olguta Buse and Richard Hind
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p051.xhtml
DOI: 10.2140/gt.2011.15.2091
(9) Geometry & Topology 15 (2011) 2111-2133
Hodge theory on nearly Kahler manifolds
by Misha Verbitsky
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p052.xhtml
DOI: 10.2140/gt.2011.15.2111
(10) Geometry & Topology 15 (2011) 2135-2180
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/2011/15-04/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 quasi-isometries of a class of solvable Lie groups I
by Irine Peng
This is the first of two consecutive papers that aim to understand
quasi-isometries of a class of unimodular split solvable Lie groups.
In the present paper, we show that locally (in a coarse sense), a
quasi-isometry 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 quasi-isometric rigidity.
(4) Coarse differentiation and quasi-isometries 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 quasi-isometries for a subclass of split
solvable unimodular Lie groups. Consequently, we show that any
finitely generated group quasi-isometric to a member of the subclass
has to be polycyclic and is virtually a lattice in an
abelian-by-abelian solvable Lie group. We also give an example of a
unimodular solvable Lie group that is not quasi-isometric to any
finitely generated group, as well deduce some quasi-isometric 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 3-manifold, 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 2m-dimensional
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 6-manifold, 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 3-space, one can associate a sequence of Laurent
polynomials, whose n-th term is the n-th colored Jones polynomial. The
paper is concerned with the asymptotic behavior of the value of the
n-th 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 n-th 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.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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