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Topic:
Thirteen papers and an erratum published by Geometry & Topology Publications
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Thirteen papers and an erratum published by Geometry & Topology Publications
Posted:
Apr 20, 2011 12:00 PM


Eleven papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 839886 Relative fixed point theory by Kate Ponto URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p025.xhtml DOI: 10.2140/agt.2011.11.839
(2) Algebraic & Geometric Topology 11 (2011) 887908 The intersecting kernels of Heegaard splittings by Fengchun Lei and Jie Wu URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p026.xhtml DOI: 10.2140/agt.2011.11.887
(3) Algebraic & Geometric Topology 11 (2011) 909928 Planar open books with four binding components by Yanki Lekili URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p027.xhtml DOI: 10.2140/agt.2011.11.909
(4) Algebraic & Geometric Topology 11 (2011) 929938 Infinite generation of noncocompact lattices on rightangled buildings by Anne Thomas and Kevin Wortman URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p028.xhtml DOI: 10.2140/agt.2011.11.929
(5) Algebraic & Geometric Topology 11 (2011) 939981 Homology of E_n ring spectra and iterated THH by Maria Basterra and Michael A Mandell URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p029.xhtml DOI: 10.2140/agt.2011.11.939
(6) Algebraic & Geometric Topology 11 (2011) 983999 Stable systolic category of the product of spheres by Hoil Ryu URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p030.xhtml DOI: 10.2140/agt.2011.11.983
(7) Algebraic & Geometric Topology 11 (2011) 10011031 The embedded contact homology of sutured solid tori by Roman Golovko URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p031.xhtml DOI: 10.2140/agt.2011.11.1001
(8) Algebraic & Geometric Topology 11 (2011) 10331052 Configurationlike spaces and coincidences of maps on orbits by R N Karasev and A Yu Volovikov URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p032.xhtml DOI: 10.2140/agt.2011.11.1033
(9) Algebraic & Geometric Topology 11 (2011) 10531076 Properties of Bott manifolds and cohomological rigidity by Suyoung Choi and Dong Youp Suh URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p033.xhtml DOI: 10.2140/agt.2011.11.1053
(10) Algebraic & Geometric Topology 11 (2011) 10771096 Symplectic manifolds with vanishing actionMaslov homomorphism by Mark Branson URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p034.xhtml DOI: 10.2140/agt.2011.11.1077
(11) Algebraic & Geometric Topology 11 (2011) 10971105 Unexpected local minima in the width complexes for knots by Alexander Zupan URL: http://www.msp.warwick.ac.uk/agt/2011/1102/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) 473498 Braid ordering and the geometry of closed braid by Tetsuya Ito URL: http://www.msp.warwick.ac.uk/gt/2011/1501/p014.xhtml DOI: 10.2140/gt.2011.15.473
(13) Geometry & Topology 15 (2011) 499500 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/2011/1501/p0C2.xhtml DOI: 10.2140/gt.2011.15.499
(14) Geometry & Topology 15 (2011) 501607 Galois actions on homotopy groups of algebraic varieties by Jonathan P Pridham URL: http://www.msp.warwick.ac.uk/gt/2011/1501/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 3manifold 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 3manifolds 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 threemanifold 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 threesphere 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 OzsvathSzabo contact invariant vanishes. As an application, we give an example of a rightveering diffeomorphism on the fourholed 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) 289311].
(4) Infinite generation of noncocompact lattices on rightangled buildings by Anne Thomas and Kevin Wortman
Let Gamma be a noncocompact lattice on a locally finite regular rightangled 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 treewalls.
(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 cuplength 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 0universal 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) Configurationlike spaces and coincidences of maps on orbits by R N Karasev and A Yu Volovikov
In this paper we study the spaces of qtuples of points in a Euclidean space, without kwise coincidences (configurationlike spaces). A transitive group action by permuting these points is considered, and some new upper bounds on the genus (in the sense of Krasnosel'skiiSchwarz and ClappPuppe) for this action are given. Some theorems of CohenLusk 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 onetwist 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 welldefined 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 actionMaslov homomorphism by Mark Branson
The actionMaslov 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) 135156], Schultens defines the width complex for a knot in order to understand the different positions a knot can occupy in the threesphere 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 NielsenThurston classification of braids and the geometric structure of the closed braid complements are in onetoone 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) 743767].
(14) Galois actions on homotopy groups of algebraic varieties by Jonathan P Pridham
We study the Galois actions on the ladic schematic and ArtinMazur homotopy groups of algebraic varieties. For proper varieties of good reduction over a local field K, we show that the ladic 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 padic schematic homotopy types. Under favourable conditions, a comparison theorem transfers all these descriptions to the ArtinMazur homotopy groups.
Geometry & Topology Publications is an imprint of Mathematical Sciences Publishers



