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Eight papers published by Geometry & Topology Publications
Posted:
Sep 5, 2011 12:24 PM


Seven papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 22372264 Simplicial volume and fillings of hyperbolic manifolds by Koji Fujiwara and Jason Fox Manning URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p073.xhtml DOI: 10.2140/agt.2011.11.2237
(2) Algebraic & Geometric Topology 11 (2011) 22652296 The entropy efficiency of pointpush mapping classes on the punctured disk by Philip Boyland and Jason Harrington URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p074.xhtml DOI: 10.2140/agt.2011.11.2265
(3) Algebraic & Geometric Topology 11 (2011) 22972318 Bounds for fixed points and fixed subgroups on surfaces and graphs by Boju Jiang, Shida Wang and Qiang Zhang URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p075.xhtml DOI: 10.2140/agt.2011.11.2297
(4) Algebraic & Geometric Topology 11 (2011) 23192368 Families of monotone symplectic manifolds constructed via symplectic cut and their Lagrangian submanifolds by Agnes Gadbled URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p076.xhtml DOI: 10.2140/agt.2011.11.2319
(5) Algebraic & Geometric Topology 11 (2011) 23692390 On the mapping space homotopy groups and the free loop space homology groups by Takahito Naito URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p077.xhtml DOI: 10.2140/agt.2011.11.2369 ` (6) Algebraic & Geometric Topology 11 (2011) 23912436 Algebraic Ktheory over the infinite dihedral group: an algebraic approach by James F Davis, Qayum Khan and Andrew Ranicki URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p078.xhtml DOI: 10.2140/agt.2011.11.2391
(7) Algebraic & Geometric Topology 11 (2011) 24372452 Free degrees of homeomorphisms on compact surfaces by Jianchun Wu and Xuezhi Zhao URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p079.xhtml DOI: 10.2140/agt.2011.11.2437
One paper has been published by Geometry & Topology
(8) Geometry & Topology 15 (2011) 15451567 Free planar actions of the Klein bottle group by Frederic Le Roux URL: http://www.msp.warwick.ac.uk/gt/2011/1503/p039.xhtml DOI: 10.2140/gt.2011.15.1545
Abstracts follow
(1) Simplicial volume and fillings of hyperbolic manifolds by Koji Fujiwara and Jason Fox Manning
Let M be a hyperbolic nmanifold whose cusps have torus cross sections. In an earlier paper, the authors constructed a variety of nonpositively and negatively curved spaces as "2pifillings" of M by replacing the cusps of M with compact "partial cones" of their boundaries. These 2pifillings are closed pseudomanifolds, and so have a fundamental class. We show that the simplicial volume of any such 2pifilling is positive, and bounded above by Vol(M)/v_n, where v_n is the volume of a regular ideal hyperbolic nsimplex. This result generalizes the fact that hyperbolic Dehn filling of a 3manifold does not increase hyperbolic volume.
In particular, we obtain information about the simplicial volumes of some 4dimensional homology spheres described by Ratcliffe and Tschantz, answering a question of Belegradek and establishing the existence of 4dimensional homology spheres with positive simplicial volume.
(2) The entropy efficiency of pointpush mapping classes on the punctured disk by Philip Boyland and Jason Harrington
We study the maximal entropy per unit generator of pointpush mapping classes on the punctured disk. Our work is motivated by fluid mixing by rods in a planar domain. If a single rod moves among N fixed obstacles, the resulting fluid diffeomorphism is in the pointpush mapping class associated with the loop in the fundamental group of the Npunctured disk traversed by the single stirrer. The collection of motions where each stirrer goes around a single obstacle generate the group of pointpush mapping classes, and the entropy efficiency with respect to these generators gives a topological measure of the mixing per unit energy expenditure of the mapping class. We give lower and upper bounds for Eff(N), the maximal efficiency in the presence of N obstacles, and prove that Eff(N) approaches log(3) as N tends to infinity. For the lower bound we compute the entropy efficiency of a specific pointpush protocol, HSP_N, which we conjecture achieves the maximum. The entropy computation uses the action on chains in a Zcovering space of the punctured disk which is designed for pointpush protocols. For the upper bound we estimate the exponential growth rate of the action of the pointpush mapping classes on the fundamental group of the punctured disk using a collection of incidence matrices and then computing the generalized spectral radius of the collection.
(3) Bounds for fixed points and fixed subgroups on surfaces and graphs by Boju Jiang, Shida Wang and Qiang Zhang
We consider selfmaps of hyperbolic surfaces and graphs, and give some bounds involving the rank and the index of fixed point classes. One consequence is a rank bound for fixed subgroups of surface group endomorphisms, similar to the BestvinaHandel bound (originally known as the Scott conjecture) for free group automorphisms.
When the selfmap is homotopic to a homeomorphism, we rely on Thurston's classification of surface automorphisms. When the surface has boundary, we work with its spine, and BestvinaHandel's theory of train track maps on graphs plays an essential role.
It turns out that the control of empty fixed point classes (for surface automorphisms) presents a special challenge. For this purpose, an alternative definition of fixed point class is introduced, which avoids covering spaces hence is more convenient for geometric discussions.
(4) Families of monotone symplectic manifolds constructed via symplectic cut and their Lagrangian submanifolds by Agnes Gadbled
We describe families of monotone symplectic manifolds constructed via the symplectic cutting procedure of Lerman [Math. Res. Lett. 2 (1995) 247258] from the cotangent bundle of manifolds endowed with a free circle action. We also give obstructions to the monotone Lagrangian embedding of some compact manifolds in these symplectic manifolds.
(5) On the mapping space homotopy groups and the free loop space homology groups by Takahito Naito
Let X be a Poincare duality space, Y a space and f a based map from X to Y. We show that the rational homotopy group of the connected component of the space of maps from X to Y containing f is contained in the rational homology group of a space L_f Y which is the pullback of f and the evaluation map from the free loop space LY to the space Y. As an application of the result, when X is a closed oriented manifold, we give a condition of a noncommutativity for the rational loop homology algebra H_{*+d}(L_f Y;Q) defined by Gruher and Salvatore which is the extension of the ChasSullivan loop homology algebra.
(6) Algebraic Ktheory over the infinite dihedral group: an algebraic approach by James F Davis, Qayum Khan and Andrew Ranicki
Two types of Nilgroups arise in the codimension 1 splitting obstruction theory for homotopy equivalences of finite CWcomplexes: the FarrellBass Nilgroups in the nonseparating case when the fundamental group is an HNN extension and the Waldhausen Nilgroups in the separating case when the fundamental group is an amalgamated free product. We obtain a general NilNil theorem in algebraic Ktheory relating the two types of Nilgroups. The infinite dihedral group is a free product and has an index 2 subgroup which is an HNN extension, so both cases arise if the fundamental group surjects onto the infinite dihedral group. The NilNil theorem implies that the two types of the reduced tildeNilgroups arising from such a fundamental group are isomorphic. There is also a topological application: in the finiteindex case of an amalgamated free product, a homotopy equivalence of finite CWcomplexes is semisplit along a separating subcomplex.
(7) Free degrees of homeomorphisms on compact surfaces by Jianchun Wu and Xuezhi Zhao
For a compact surface M, the free degree fr(M) of homeomorphisms on M is the minimum positive integer n with property that for any self homeomorphism xi of M, at least one of the iterates xi,xi^2,...,xi^n has a fixed point. This is to say fr(M) is the maximum of least periods among all periodic points of self homeomorphisms on M. We prove that fr(F_{g,b}) is at most 24g24 for g at least 2 and fr(N_{g,b}) is at most 12g24 for g at least 3.
(8) Free planar actions of the Klein bottle group by Frederic Le Roux
We describe the structure of the free actions of the fundamental group of the Klein bottle <a,baba^{1}=b^{1}> by orientation preserving homeomorphisms of the plane. The main result is that a must act properly discontinuously, while b cannot act properly discontinuously. As a corollary, we describe some torsion free groups that may not act freely on the plane. We also find some properties which are reminiscent of Brouwer theory for the integers, in particular that every free action is virtually wandering.
Geometry & Topology Publications is an imprint of Mathematical Sciences Publishers



