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Thirteen papers and an erratum published by Geometry & Topology Publications
Posted:
Apr 20, 2011 12:00 PM
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Eleven papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 839-886
Relative fixed point theory
by Kate Ponto
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p025.xhtml
DOI: 10.2140/agt.2011.11.839
(2) Algebraic & Geometric Topology 11 (2011) 887-908
The intersecting kernels of Heegaard splittings
by Fengchun Lei and Jie Wu
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p026.xhtml
DOI: 10.2140/agt.2011.11.887
(3) Algebraic & Geometric Topology 11 (2011) 909-928
Planar open books with four binding components
by Yanki Lekili
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p027.xhtml
DOI: 10.2140/agt.2011.11.909
(4) Algebraic & Geometric Topology 11 (2011) 929-938
Infinite generation of non-cocompact lattices on right-angled buildings
by Anne Thomas and Kevin Wortman
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p028.xhtml
DOI: 10.2140/agt.2011.11.929
(5) Algebraic & Geometric Topology 11 (2011) 939-981
Homology of E_n ring spectra and iterated THH
by Maria Basterra and Michael A Mandell
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p029.xhtml
DOI: 10.2140/agt.2011.11.939
(6) Algebraic & Geometric Topology 11 (2011) 983-999
Stable systolic category of the product of spheres
by Hoil Ryu
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p030.xhtml
DOI: 10.2140/agt.2011.11.983
(7) Algebraic & Geometric Topology 11 (2011) 1001-1031
The embedded contact homology of sutured solid tori
by Roman Golovko
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p031.xhtml
DOI: 10.2140/agt.2011.11.1001
(8) Algebraic & Geometric Topology 11 (2011) 1033-1052
Configuration-like spaces and coincidences of maps on orbits
by R N Karasev and A Yu Volovikov
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p032.xhtml
DOI: 10.2140/agt.2011.11.1033
(9) Algebraic & Geometric Topology 11 (2011) 1053-1076
Properties of Bott manifolds and cohomological rigidity
by Suyoung Choi and Dong Youp Suh
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p033.xhtml
DOI: 10.2140/agt.2011.11.1053
(10) Algebraic & Geometric Topology 11 (2011) 1077-1096
Symplectic manifolds with vanishing action-Maslov homomorphism
by Mark Branson
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p034.xhtml
DOI: 10.2140/agt.2011.11.1077
(11) Algebraic & Geometric Topology 11 (2011) 1097-1105
Unexpected local minima in the width complexes for knots
by Alexander Zupan
URL: http://www.msp.warwick.ac.uk/agt/2011/11-02/p035.xhtml
DOI: 10.2140/agt.2011.11.1097
Two papers and an erratum have been published by Geometry & Topology
(12) Geometry & Topology 15 (2011) 473-498
Braid ordering and the geometry of closed braid
by Tetsuya Ito
URL: http://www.msp.warwick.ac.uk/gt/2011/15-01/p014.xhtml
DOI: 10.2140/gt.2011.15.473
(13) Geometry & Topology 15 (2011) 499-500
Erratum to the article
A simply connected surface of general type with p_g=0 and K^2=3
by Heesang Park, Jongil Park and Dongsoo Shin
URL: http://www.msp.warwick.ac.uk/gt/2011/15-01/p0C2.xhtml
DOI: 10.2140/gt.2011.15.499
(14) Geometry & Topology 15 (2011) 501-607
Galois actions on homotopy groups of algebraic varieties
by Jonathan P Pridham
URL: http://www.msp.warwick.ac.uk/gt/2011/15-01/p016.xhtml
DOI: 10.2140/gt.2011.15.501
Abstracts follow
(1) Relative fixed point theory
by Kate Ponto
The Lefschetz fixed point theorem and its converse have many
generalizations. One of these generalizations is to endomorphisms of
a space relative to a fixed subspace. In this paper we define
relative Lefschetz numbers and Reidemeister traces using traces in
bicategories with shadows. We use the functoriality of this trace to
identify different forms of these invariants and to prove a relative
Lefschetz fixed point theorem and its converse.
(2) The intersecting kernels of Heegaard splittings
by Fengchun Lei and Jie Wu
The paper is principally concerned with the intersecting kernel of a
Heegaard splitting for a closed 3-manifold M. By observing that the
second homotopy group of M is a canonical quotient group of the
intersecting kernel, our first result is to algebraically give an
exact sequence of the modules over pi_1(M) concerning pi_2(M), which
is derived from the Fox derivatives related to the gluing data of the
Heegaard splitting. As a consequence, we give an algebraic criterion
on the irreducibility of 3-manifolds from Heegaard splittings. Our
second main result describes the intersecting kernel of the Heegaard
splittings for connected sums.
(3) Planar open books with four binding components
by Yanki Lekili
We study an explicit construction of planar open books with four
binding components on any three-manifold which is given by integral
surgery on three component pure braid closures. This construction is
general, indeed any planar open book with four binding components is
given this way. Using this construction and results on exceptional
surgeries on hyperbolic links, we show that any contact structure of
the three-sphere supports a planar open book with four binding
components, determining the minimal number of binding components
needed for planar open books supporting these contact structures. In
addition, we study a class of monodromies of a planar open book with
four binding components in detail. We characterize all the
symplectically fillable contact structures in this class and we
determine when the Ozsvath--Szabo contact invariant vanishes. As an
application, we give an example of a right-veering diffeomorphism on
the four-holed sphere which is not destabilizable and yet supports an
overtwisted contact structure. This provides a counterexample to a
conjecture of Honda, Kazez and Matic from [J. Differential Geom. 83
(2009) 289--311].
(4) Infinite generation of non-cocompact lattices on right-angled buildings
by Anne Thomas and Kevin Wortman
Let Gamma be a non-cocompact lattice on a locally finite regular
right-angled building X. We prove that if Gamma has a strict
fundamental domain then Gamma is not finitely generated. We use the
separation properties of subcomplexes of X called tree-walls.
(5) Homology of E_n ring spectra and iterated THH
by Maria Basterra and Michael A Mandell
We describe an iterable construction of THH for an E_n ring
spectrum. The reduced version is an iterable bar construction and its
nth iterate gives a model for the shifted cotangent complex at the
augmentation, representing reduced topological Quillen homology of an
augmented E_n algebra.
(6) Stable systolic category of the product of spheres
by Hoil Ryu
The stable systolic category of a closed manifold M indicates the
complexity in the sense of volume. This is a homotopy invariant,
even though it is defined by some relations between homological volumes
on M. We show an equality of the stable systolic category and the real
cup-length for the product of arbitrary finite dimensional real homology
spheres. Also we prove the invariance of the stable systolic category
under the rational equivalences for orientable 0-universal manifolds.
(7) The embedded contact homology of sutured solid tori
by Roman Golovko
We calculate the relative versions of embedded contact homology,
contact homology and cylindrical contact homology of the sutured solid
torus (S^1 x D^2, Gamma), where Gamma consists of 2n parallel
longitudinal sutures.
(8) Configuration-like spaces and coincidences of maps on orbits
by R N Karasev and A Yu Volovikov
In this paper we study the spaces of q-tuples of points in a Euclidean
space, without k-wise coincidences (configuration-like spaces). A
transitive group action by permuting these points is considered, and some
new upper bounds on the genus (in the sense of Krasnosel'skii--Schwarz and
Clapp--Puppe) for this action are given. Some theorems of Cohen--Lusk type
for coincidence points of continuous maps to Euclidean spaces are deduced.
(9) Properties of Bott manifolds and cohomological rigidity
by Suyoung Choi and Dong Youp Suh
The cohomological rigidity problem for toric manifolds asks whether the
integral cohomology ring of a toric manifold determines the topological
type of the manifold. In this paper, we consider the problem with the
class of one-twist Bott manifolds to get an affirmative answer to the
problem. We also generalize the result to quasitoric manifolds. In doing
so, we show that the twist number of a Bott manifold is well-defined and
is equal to the cohomological complexity of the cohomology ring of the
manifold. We also show that any cohomology Bott manifold is homeomorphic
to a Bott manifold. All these results are also generalized to the case
with Z_(2)-coefficients, where Z_(2) is the localized ring at 2.
(10) Symplectic manifolds with vanishing action-Maslov homomorphism
by Mark Branson
The action--Maslov homomorphism I: pi_1(Ham(X,omega)) --> R is an
important tool for understanding the topology of the Hamiltonian group of
monotone symplectic manifolds. We explore conditions for the vanishing
of this homomorphism, and show that it is identically zero when the
Seidel element has finite order and the homology satisfies property D
(a generalization of having homology generated by divisor classes).
We use these results to show that I=0 for products of projective spaces
and the Grassmannian of 2 planes in C^4.
(11) Unexpected local minima in the width complexes for knots
by Alexander Zupan
In [Pacific J. Math. 239 (2009) 135--156], Schultens defines the width
complex for a knot in order to understand the different positions a
knot can occupy in the three-sphere and the isotopies between these
positions. She poses several questions about these width complexes;
in particular, she asks whether the width complex for a knot can have
local minima that are not global minima. In this paper, we find an
embedding of the unknot 0_1 that is a local minimum but not a global
minimum in the width complex for 0_1, resolving a question of
Scharlemann. We use this embedding to exhibit for any knot K
infinitely many distinct local minima that are not global minima of
the width complex for K.
(12) Braid ordering and the geometry of closed braid
by Tetsuya Ito
We study the relationships between the Dehornoy ordering of the braid groups
and the topology and geometry of the closed braid complements. We show that the
Dehornoy floor of braids, which is a nonnegative integer determined by the
Dehornoy ordering, tells us the position of essential surfaces in the closed
braid complements. Furthermore, we prove that if the Dehornoy floor of a braid
is bigger than or equal to two, then the Nielsen-Thurston classification of
braids and the geometric structure of the closed braid complements are in
one-to-one correspondence.
(13) Erratum to the article
A simply connected surface of general type with p_g=0 and K^2=3
by Heesang Park, Jongil Park and Dongsoo Shin
We give a different configuration constructed from a rational elliptic surface
to correct an example from [Geom. Topol. 13 (2009) 743-767].
(14) Galois actions on homotopy groups of algebraic varieties
by Jonathan P Pridham
We study the Galois actions on the l-adic schematic and Artin-Mazur
homotopy groups of algebraic varieties. For proper varieties of good
reduction over a local field K, we show that the l-adic schematic
homotopy groups are mixed representations explicitly determined by the
Galois action on cohomology of Weil sheaves, whenever l is not equal
to the residue characteristic p of K. For quasiprojective varieties of
good reduction, there is a similar characterisation involving the
Gysin spectral sequence. When l=p, a slightly weaker result is proved
by comparing the crystalline and p-adic schematic homotopy
types. Under favourable conditions, a comparison theorem transfers all
these descriptions to the Artin-Mazur homotopy groups.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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