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Nine papers published by Geometry & Topology Publications
Posted:
Aug 10, 2011 12:58 PM
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Three papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 2167-2190
An algorithm for finding parameters of tunnels
by Kai Ishihara
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p070.xhtml
DOI: 10.2140/agt.2011.11.2167
(2) Algebraic & Geometric Topology 11 (2011) 2191-2205
Quantum invariants of random 3-manifolds
by Nathan M Dunfield and Helen Wong
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p071.xhtml
DOI: 10.2140/agt.2011.11.2191
(3) Algebraic & Geometric Topology 11 (2011) 2207-2235
Flat structures on surface bundles
by Jonathan Bowden
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p072.xhtml
DOI: 10.2140/agt.2011.11.2207
Six papers have been published by Geometry & Topology
(4) Geometry & Topology 15 (2011) 1225-1295
Connected components of the compactification of representation
spaces of surface groups
by Maxime Wolff
URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p033.xhtml
DOI: 10.2140/gt.2011.15.1225
(5) Geometry & Topology 15 (2011) 1297-1312
Minimal pseudo-Anosov translation lengths on the complex of curves
by Vaibhav Gadre and Chia-Yen Tsai
URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p034.xhtml
DOI: 10.2140/gt.2011.15.1297
(6) Geometry & Topology 15 (2011) 1313-1417
Deformed Hamiltonian Floer theory, capacity estimates and Calabi
quasimorphisms
by Michael Usher
URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p035.xhtml
DOI: 10.2140/gt.2011.15.1313
(7) Geometry & Topology 15 (2011) 1419-1475
Line patterns in free groups
by Christopher H Cashen and Natasa Macura
URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p036.xhtml
DOI: 10.2140/gt.2011.15.1419
(8) Geometry & Topology 15 (2011) 1477-1508
Isosystolic genus three surfaces critical for slow metric variations
by Stephane Sabourau
URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p037.xhtml
DOI: 10.2140/gt.2011.15.1477
(9) Geometry & Topology 15 (2011) 1509-1543
Non-commutative Donaldson-Thomas theory and vertex operators
by Kentaro Nagao
URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p038.xhtml
DOI: 10.2140/gt.2011.15.1509
Abstracts follow
(1) An algorithm for finding parameters of tunnels
by Kai Ishihara
Cho and McCullough gave a numerical parameterization of the collection
of all
tunnels of all tunnel number 1 knots and links in the 3-sphere. Here we
give an algorithm for finding the parameter of a given tunnel by using
its
Heegaard diagram.
(2) Quantum invariants of random 3-manifolds
by Nathan M Dunfield and Helen Wong
We consider the SO(3) Witten-Reshetikhin-Turaev quantum invariants of
random 3-manifolds. When the level r is prime, we show that the
asymptotic distribution of the absolute value of these invariants is
given by a Rayleigh distribution which is independent of the choice of
level. Hence the probability that the quantum invariant certifies the
Heegaard genus of a random 3-manifold of a fixed Heegaard genus g is
positive but very small, less than 10^-7 except when g<=3. We also
examine random surface bundles over the circle and find the same
distribution for quantum invariants there.
(3) Flat structures on surface bundles
by Jonathan Bowden
We show that there exist flat surface bundles with closed leaves having
nontrivial normal bundles. This leads us to compute the abelianisation
of
surface diffeomorphism groups with marked points. We also extend a
formula of
Tsuboi that expresses the Euler class of a flat circle bundle in terms
of the
Calabi invariant of certain Hamiltonian diffeomorphisms to surfaces of
higher
genus and derive a similar formula for the first MMM-class of surface
bundles
with punctured fibre.
(4) Connected components of the compactification of representation
spaces of surface groups
by Maxime Wolff
The Thurston compactification of Teichmuller spaces has been
generalised to many different representation spaces by Morgan, Shalen,
Bestvina, Paulin, Parreau and others. In the simplest case of
representations of fundamental groups of closed hyperbolic surfaces in
PSL(2,R), we prove that this compactification behaves very badly: the
nice behaviour of the Thurston compactification of the Teichmuller
space contrasts with wild phenomena happening on the boundary of the
other connected components of these representation spaces. We prove
that it is more natural to consider a refinement of this
compactification, which remembers the orientation of the hyperbolic
plane. The ideal points of this compactification are oriented R-trees,
ie, R-trees equipped with a planar structure.
(5) Minimal pseudo-Anosov translation lengths on the complex of curves
by Vaibhav Gadre and Chia-Yen Tsai
We establish bounds on the minimal asymptotic pseudo-Anosov
translation lengths on the complex of curves of orientable
surfaces. In particular, for a closed surface with genus g at least 2,
we show that there are positive constants a_1 < a_2 such that the
minimal translation length is bounded below and above by a_1/g^2 and
a_2/g^2.
(6) Deformed Hamiltonian Floer theory, capacity estimates and Calabi
quasimorphisms
by Michael Usher
We develop a family of deformations of the differential and of the
pair-of-pants product on the Hamiltonian Floer complex of a symplectic
manifold (M,omega) which upon passing to homology yields ring
isomorphisms with the *big* quantum homology of M. By studying the
properties of the resulting deformed version of the Oh-Schwarz
spectral invariants, we obtain a Floer-theoretic interpretation of a
result of Lu which bounds the Hofer-Zehnder capacity of M when M has a
nonzero Gromov-Witten invariant with two point constraints, and we
produce a new algebraic criterion for (M,omega) to admit a Calabi
quasimorphism and a symplectic quasistate. This latter criterion is
found to hold whenever M has generically semisimple quantum homology
in the sense considered by Dubrovin and Manin (this includes all
compact toric M), and also whenever M is a point blowup of an
arbitrary closed symplectic manifold.
(7) Line patterns in free groups
by Christopher H Cashen and Natasa Macura
We study line patterns in a free group by considering the topology of
the decomposition space, a quotient of the boundary at infinity of the
free group related to the line pattern. We show that the group of
quasi-isometries preserving a line pattern in a free group acts by
isometries on a related space if and only if there are no cut pairs in
the decomposition space. We also give an algorithm to detect such cut
pairs.
(8) Isosystolic genus three surfaces critical for slow metric variations
by Stephane Sabourau
We show that the two piecewise flat surfaces with conical
singularities conjectured by E Calabi as extremal surfaces for the
isosystolic problem in genus 3 are critical with respect to some
metric variations. The proof relies on a new approach to study
isosystolic extremal surfaces.
(9) Non-commutative Donaldson-Thomas theory and vertex operators
by Kentaro Nagao
In [K Nagao, Refined open non-commutative Donaldson--Thomas theory
for small toric Calabi-Yau 3-folds, Pacific J. Math. (to appear),
arXiv:0907.3784], we introduced a variant of non-commutative
Donaldson-Thomas theory in a combinatorial way, which is related to the
topological vertex by a wall-crossing phenomenon. In this paper, we (1)
provide an alternative definition in a geometric way, (2) show that the
two definitions agree with each other and (3) compute the invariants
using the vertex operator method, following [A Okounkov, N Reshetikhin,
C Vafa, Quantum Calabi-Yau and classical crystals, from: "The unity
of mathematics", Progr. Math., Birkhauser (2006) 597--618] and [B Young,
Generating functions for colored 3D Young diagrams and the
Donaldson-Thomas invariants of orbifolds, Duke Math. J. 152 (2010)
115--153]. The stability parameter in the geometric definition
determines the order of the vertex operators and hence we can understand
the wall-crossing formula in non-commutative Donaldson-Thomas theory as
the commutator relation of the vertex operators.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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