Twelve papers published or posted by Geometry & Topology Publications
Geometry and Topology
(1) Algebraic & Geometric Topology 9 (2009) 2041-2054
Amalgamations of Heegaard splittings in 3-manifolds
without some essential surfaces
by Guoqiu Yang and Fengchun Lei
URL: http://www.msp.warwick.ac.uk/agt/2009/09-04/p069.xhtml
DOI: 10.2140/agt.2009.9.2041
(2) Algebraic & Geometric Topology 9 (2009) 2055-2077
Injective simplicial maps of the complex of arcs on nonorientable surfaces
by Elmas Irmak
URL: http://www.msp.warwick.ac.uk/agt/2009/09-04/p070.xhtml
DOI: 10.2140/agt.2009.9.2055
(3) Algebraic & Geometric Topology 9 (2009) 2079-2100
A new characterization of Conrad's property for group orderings,
with applications
by Andrs Navas and Cristobal Rivas
Appendix: Adam Clay
URL: http://www.msp.warwick.ac.uk/agt/2009/09-04/p071.xhtml
DOI: 10.2140/agt.2009.9.2079
(4) Algebraic & Geometric Topology 9 (2009) 2101-2120
Hyperbolic groups which fiber in infinitely many ways
by TaraLee Mecham and Antara Mukherjee
URL: http://www.msp.warwick.ac.uk/agt/2009/09-04/p072.xhtml
DOI: 10.2140/agt.2009.9.2101
(5) Algebraic & Geometric Topology 9 (2009) 2121-2174
Converting between quadrilateral and standard
solution sets in normal surface theory
by Benjamin A Burton
URL: http://www.msp.warwick.ac.uk/agt/2009/09-04/p073.xhtml
DOI: 10.2140/agt.2009.9.2121
(6) Algebraic & Geometric Topology 9 (2009) 2175-2189
Depth of pleated surfaces in toroidal cusps of hyperbolic 3-manifolds
by Ying-Qing Wu
URL: http://www.msp.warwick.ac.uk/agt/2009/09-04/p074.xhtml
DOI: 10.2140/agt.2009.9.2175
(7) Algebraic & Geometric Topology 9 (2009) 2191-2201
A smallest irreducible lattice in the product of trees
by David Janzen and Daniel T Wise
URL: http://www.msp.warwick.ac.uk/agt/2009/09-04/p075.xhtml
DOI: 10.2140/agt.2009.9.2191
(8) Algebraic & Geometric Topology 9 (2009) 2203-2223
Symplectic surgeries and normal surface singularities
by David T Gay and Andras I Stipsicz
URL: http://www.msp.warwick.ac.uk/agt/2009/09-04/p076.xhtml
DOI: 10.2140/agt.2009.9.2203
(9) Algebraic & Geometric Topology 9 (2009) 2225-2246
A combinatorial approach to surgery formulas in Heegaard Floer homology
by Eaman Eftekhary
URL: http://www.msp.warwick.ac.uk/agt/2009/09-04/p077.xhtml
DOI: 10.2140/agt.2009.9.2225
Three papers have been posted in preview by Geometry & Topology
(10) Geometry & Topology 14 (2010) 193-242
Canonical triangulations of Dehn fillings
by Francois Gueritaud and Saul Schleimer
URL: http://www.msp.warwick.ac.uk/gt/2010/14-01/p005.xhtml
DOI: 10.2140/gt.2010.14.193
(11) Geometry & Topology 14 (2010) 243-275
An elementary construction of Anick's fibration
by Brayton Gray and Stephen Theriault
URL: http://www.msp.warwick.ac.uk/gt/2010/14-01/p006.xhtml
DOI: 10.2140/gt.2010.14.243
(12) Geometry & Topology 14 (2010) 277-392
Prescribing the behaviour of geodesics in negative curvature
by Jouni Parkkonen and Frederic Paulin
URL: http://www.msp.warwick.ac.uk/gt/2010/14-01/p007.xhtml
DOI: 10.2140/gt.2010.14.277
Abstracts follow
(1) Amalgamations of Heegaard splittings in 3-manifolds without
some essential surfaces
by Guoqiu Yang and Fengchun Lei
Let M be a compact, orientable, boundary-irreducible 3-manifold and F
be a connected closed essential surface in M with g(F) at least 1
which cuts M into M_1 and M_2. In the present paper, we show the
following theorem: Suppose that there is no essential surface with
boundary (Q_i,partial Q_i) in (M_i,F) satisfying chi(Q_i) > 2 + g(F) -
2g(M_i), i=1,2. Then g(M) = g(M_1) + g(M_2) - g(F). As a consequence,
we further show that if M_i has a Heegaard splitting along S_i with
distance D(S_i) at least 2g(M_i)-g(F), i=1,2, then g(M) = g(M_1) +
g(M_2) - g(F).
The main results follow from a new technique which is a stronger
version of Schultens' Lemma.
(2) Injective simplicial maps of the complex of arcs on nonorientable surfaces
by Elmas Irmak
We prove that each injective simplicial map from the complex of arcs
of a compact, connected, nonorientable surface with nonempty boundary
to itself is induced by a homeomorphism of the surface. We also prove
that the automorphism group of the arc complex is isomorphic to the
quotient of the mapping class group of the surface by its center.
(3) A new characterization of Conrad's property for group orderings,
with applications
by Andrs Navas and Cristobal Rivas
Appendix: Adam Clay
We provide a pure algebraic version of the first-named author's dynamical
characterization of the Conrad property for group orderings. This approach
allows dealing with general group actions on totally ordered spaces. As
an application, we give a new and somehow constructive proof of a theorem
first established by Linnell: an orderable group having infinitely many
orderings has uncountably many. This proof is achieved by extending
to uncountable orderable groups a result about orderings which may be
approximated by their conjugates. This last result is illustrated by
an example of an exotic ordering on the free group given by the third
author in the Appendix.
(4) Hyperbolic groups which fiber in infinitely many ways
by TaraLee Mecham and Antara Mukherjee
We construct examples of CAT(0), free-by-cyclic, hyperbolic groups
which fiber in infinitely many ways over Z. The construction involves
adding a specialized square 2-cell to a non-positively curved, squared
2-complex defined by labeled oriented graphs. The fundamental groups of
the resulting complexes are CAT(0), hyperbolic, free-by-cyclic and can
be mapped onto Z in infinitely many ways.
(5) Converting between quadrilateral and standard
solution sets in normal surface theory
by Benjamin A Burton
The enumeration of normal surfaces is a crucial but very slow
operation in algorithmic 3-manifold topology. At the heart of this
operation is a polytope vertex enumeration in a high-dimensional
space (standard coordinates). Tollefson's Q-theory speeds up this
operation by using a much smaller space (quadrilateral coordinates),
at the cost of a reduced solution set that might not always be
sufficient for our needs.
In this paper we present algorithms for converting between solution
sets in quadrilateral and standard coordinates.
As a consequence we obtain a new algorithm for enumerating all
standard vertex normal surfaces, yielding both the
speed of quadrilateral coordinates and the wider applicability of
standard coordinates. Experimentation
with the software package emphRegina shows this new algorithm
to be extremely fast in practice, improving speed for large cases by
factors from thousands up to millions.
(6) Depth of pleated surfaces in toroidal cusps of hyperbolic 3-manifolds
by Ying-Qing Wu
Let F be a closed essential surface in a hyperbolic
3-manifold M with a toroidal cusp N. The depth of F in N is
the maximal distance from points of F in N to the boundary of N.
It will be shown that if F is an essential pleated surface which is
not coannular to the boundary torus of N then the depth of F in
N is bounded above by a constant depending only on the genus of
F. The result is used to show that an immersed closed essential
surface in M which is not coannular to the torus boundary components
of M will remain essential in the Dehn filling manifold M(gamma)
after excluding C_g curves from each torus boundary component of
M, where C_g is a constant depending only on the genus g of the
surface.
(7) A smallest irreducible lattice in the product of trees
by David Janzen and Daniel T Wise
We produce a nonpositively curved square complex X containing exactly
four squares. Its universal cover X-tilde is isomorphic to the
product of two 4-valent trees. The fundamental group of X is a lattice
in Aut(X-tilde) but is not virtually a nontrivial product of free
groups. There is no such example with fewer than four squares. The
main ingredient in our analysis is that X-tilde contains an
"anti-torus" which is a certain aperiodically tiled plane.
(8) Symplectic surgeries and normal surface singularities
by David T Gay and Andras I Stipsicz
We show that every negative definite configuration of symplectic
surfaces in a symplectic 4-manifold has a strongly symplectically
convex neighborhood. We use this to show that if a negative definite
configuration satisfies an additional negativity condition at each
surface in the configuration and if the complex singularity with
resolution diffeomorphic to a neighborhood of the configuration has a
smoothing, then the configuration can be symplectically replaced by
the smoothing of the singularity. This generalizes the symplectic
rational blowdown procedure used in recent constructions of small
exotic 4-manifolds.
(9) A combinatorial approach to surgery formulas in Heegaard Floer homology
by Eaman Eftekhary
Using the combinatorial approach to Heegaard Floer homology, we obtain
a relatively easy formula for computation of the groups
hatHF(Y_{p/q}(K),Z/2Z), where Y_{p/q}(K) is the three-manifold
obtained by p/q-surgery on a knot K inside a homology sphere Y.
(10) Canonical triangulations of Dehn fillings
by Francois Gueritaud and Saul Schleimer
Every cusped, finite-volume hyperbolic three-manifold has a canonical
decomposition into ideal polyhedra. We study the canonical
decomposition of the hyperbolic manifold obtained by filling some (but
not all) of the cusps with solid tori: in a broad range of cases,
generic in an appropriate sense, this decomposition can be predicted
from that of the unfilled manifold (a similar result has been
independently announced by [Kokyuroku 1329, RIMS, Kyoto (2003)
121-132]). We also find the canonical decompositions of all hyperbolic
Dehn fillings on one cusp of the Whitehead link complement.
(11) An elementary construction of Anick's fibration
by Brayton Gray and Stephen Theriault
Cohen, Moore, and Neisendorfer's work on the odd primary homotopy
theory of spheres and Moore spaces, as well as the first author's
work on the secondary suspension, predicted the existence of a
p-local fibration S^2n-1 -> T -> \Omega S^2n+1
whose connecting map is degree p^r. In a long and
complex monograph, Anick constructed such a fibration for p >= 5
and r >= 1. Using new methods we give a much more conceptual
construction which is also valid for p=3 and r >= 1. We go on
to establish an H space structure on T_{2n-1} and use this to
construct a secondary EHP sequence for the Moore space spectrum.
(12) Prescribing the behaviour of geodesics in negative curvature
by Jouni Parkkonen and Frederic Paulin
Given a family of (almost) disjoint strictly convex subsets of a
complete negatively curved Riemannian manifold M, such as balls,
horoballs, tubular neighbourhoods of totally geodesic submanifolds,
etc, the aim of this paper is to construct geodesic rays or lines in M
which have exactly once an exactly prescribed (big enough) penetration
in one of them, and otherwise avoid (or do not enter too much into)
them. Several applications are given, Several applications are given,
including a definite improvement of the unclouding problem of of our
paper [Geom. Func. Anal. 15 (2005) 491--533], the prescription of
heights of geodesic lines in a finite volume such M, or of spiraling
times around a closed geodesic in a closed such M. We also prove that
the Hall ray phenomenon described by Hall in special arithmetic
situations and by Schmidt-Sheingorn for hyperbolic surfaces is in fact
only a negative curvature property.