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Fifteen papers published by Geometry & Topology Publications
Posted:
Mar 20, 2012 12:00 PM


Thirteen papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 12 (2012) 131153 Indecomposable PD_3complexes by Jonathan A Hillman URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p008.xhtml DOI: 10.2140/agt.2012.12.131
(2) Algebraic & Geometric Topology 12 (2012) 155213 Locally symmetric spaces and Ktheory of number fields by Thilo Kuessner URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p009.xhtml DOI: 10.2140/agt.2012.12.155
(3) Algebraic & Geometric Topology 12 (2012) 215233 On volumes of hyperbolic orbifolds by Ilesanmi Adeboye and Guofang Wei URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p010.xhtml DOI: 10.2140/agt.2012.12.215
(4) Algebraic & Geometric Topology 12 (2012) 235265 Generalized Momstructures and ideal triangulations of 3manifolds with nonspherical boundary by Ekaterina Pervova URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p011.xhtml DOI: 10.2140/agt.2012.12.235
(5) Algebraic & Geometric Topology 12 (2012) 267291 Lagrangian mapping class groups from a group homological point of view by Takuya Sakasai URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p012.xhtml DOI: 10.2140/agt.2012.12.267
(6) Algebraic & Geometric Topology 12 (2012) 293305 A note on Gornik's perturbation of KhovanovRozansky homology by Andrew Lobb URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p013.xhtml DOI: 10.2140/agt.2012.12.293
(7) Algebraic & Geometric Topology 12 (2012) 307342 Spectra associated to symmetric monoidal bicategories by Angelica M Osorno URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p014.xhtml DOI: 10.2140/agt.2012.12.307
(8) Algebraic & Geometric Topology 12 (2012) 343413 Higher cohomologies of modules by Maria Calvo, Antonio M Cegarra and Nguyen T Quang URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p015.xhtml DOI: 10.2140/agt.2012.12.343
(9) Algebraic & Geometric Topology 12 (2012) 415420 Noninjectivity of the ``hair'' map by Bertrand PatureauMirand URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p016.xhtml DOI: 10.2140/agt.2012.12.415
(10) Algebraic & Geometric Topology 12 (2012) 421433 Bounded orbits and global fixed points for groups acting on the plane by Kathryn Mann URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p017.xhtml DOI: 10.2140/agt.2012.12.421
(11) Algebraic & Geometric Topology 12 (2012) 435448 LusternikSchnirelmann category and the connectivity of X by Nicholas A Scoville URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p018.xhtml DOI: 10.2140/agt.2012.12.435
(12) Algebraic & Geometric Topology 12 (2012) 449467 Some bounds for the knot Floer auinvariant of satellite knots by Lawrence P Roberts URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p019.xhtml DOI: 10.2140/agt.2012.12.449
(13) Algebraic & Geometric Topology 12 (2012) 469492 Associahedra and weak monoidal structures on categories by Zbigniew Fiedorowicz, Steven Gubkin and Rainer M Vogt URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p020.xhtml DOI: 10.2140/agt.2012.12.469
Two papers have been published by Geometry & Topology
(14) Geometry & Topology 16 (2012) 391432 A cohomological characterisation of Yu's property A for metric spaces by Jacek Brodzki, Graham A Niblo and Nick Wright URL: http://www.msp.warwick.ac.uk/gt/2012/1601/p007.xhtml DOI: 10.2140/gt.2012.16.391
(15) Geometry & Topology 16 (2012) 433473 Chow rings and decomposition theorems for families of K!3 surfaces and CalabiYau hypersurfaces by Claire Voisin URL: http://www.msp.warwick.ac.uk/gt/2012/1601/p008.xhtml DOI: 10.2140/gt.2012.16.433
Abstracts follow
(1) Indecomposable PD_3complexes by Jonathan A Hillman
We show that if X is an indecomposable PD_3complex and pi_1(X) is the fundamental group of a reduced finite graph of finite groups but is neither Z nor Z+Z/2Z then X is orientable, the underlying graph is a tree, the vertex groups have cohomological period dividing 4 and all but at most one of the edge groups is Z/2Z. If there are no exceptions then all but at most one of the vertex groups is dihedral of order 2m with m odd. Every such group is realized by some PD_3complex. Otherwise, one edge group may be Z/6Z. We do not know of any such examples.
We also ask whether every PD_3complex has a finite covering space which is homotopy equivalent to a closed orientable 3manifold, and we propose a strategy for tackling this question.
(2) Locally symmetric spaces and Ktheory of number fields by Thilo Kuessner
For a closed locally symmetric space M=Gamma \ G/K and a representation rho from G to GL(N,C) we consider the pushforward of the fundamental class in H_*(BGL(overline{Q})) and a related invariant in K_*(overline{Q}) otimes Q. We discuss the nontriviality of this invariant and we generalize the construction to cusped locally symmetric spaces of Rrank one.
(3) On volumes of hyperbolic orbifolds by Ilesanmi Adeboye and Guofang Wei
We use HC Wang's bound on the radius of a ball embedded in the fundamental domain of a lattice of a semisimple Lie group to construct an explicit lower bound for the volume of a hyperbolic norbifold.
(4) Generalized Momstructures and ideal triangulations of 3manifolds with nonspherical boundary by Ekaterina Pervova
The socalled Momstructures on hyperbolic cusped 3manifolds without boundary were introduced by Gabai, Meyerhoff, and Milley, and used by them to identify the smallest closed hyperbolic manifold. In this work we extend the notion of a Momstructure to include the case of 3manifolds with nonempty boundary that does not have spherical components. We then describe a certain relation between such generalized Momstructures, called protoMomstructures, internal on a fixed 3manifold N, and ideal triangulations of N; in addition, in the case of nonclosed hyperbolic manifolds without annular cusps, we describe how an internal geometric protoMomstructure can be constructed starting from the EpsteinPenner or Kojima decomposition. Finally, we exhibit a set of combinatorial moves that relate any two internal protoMomstructures on a fixed N to each other.
(5) Lagrangian mapping class groups from a group homological point of view by Takuya Sakasai
We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups, called Lagrangian mapping class groups, are known to play important roles in the interaction between the mapping class group and finitetype invariants of 3manifolds. In this paper, we discuss these groups from a group (co)homological point of view. The results include the determination of their abelianizations, lower bounds of the second homology and remarks on the (co)homology of higher degrees. As a byproduct of this investigation, we determine the second homology of the mapping class group of a surface of genus 3.
(6) A note on Gornik's perturbation of KhovanovRozansky homology by Andrew Lobb
We show that the information contained in the associated graded vector space to Gornik's version of KhovanovRozansky knot homology is equivalent to a single even integer s_n(K). Furthermore we show that s_n is a homomorphism from the smooth knot concordance group to the integers. This is in analogy with Rasmussen's invariant coming from a perturbation of Khovanov homology.
(7) Spectra associated to symmetric monoidal bicategories by Angelica M Osorno
We show how to construct a Gammabicategory from a symmetric monoidal bicategory and use that to show that the classifying space is an infinite loop space upon group completion. We also show a way to relate this construction to the classic Gammacategory construction for a permutative category. As an example, we use this machinery to construct a delooping of the Ktheory of a rig category as defined by Baas, Dundas and Rognes [London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 1845].
(8) Higher cohomologies of modules by Maria Calvo, Antonio M Cegarra and Nguyen T Quang
If C is a small category, then a right Cmodule is a contravariant functor from C into abelian groups. The abelian category Mod_C of right Cmodules has enough projective and injective objects, and the groups Ext^n_Mod_C(B,A) provide the basic cohomology theory for Cmodules. In this paper we introduce, for each integer r>0, an approach for a levelr cohomology theory for Cmodules by defining cohomology groups H^n_{C,r}(B,A), n>=0, whose study this article is mainly dedicated to. Applications to the homotopy classification of braided and symmetric Cfibred categorical groups and their homomorphisms are given.
(9) Noninjectivity of the ``hair'' map by Bertrand PatureauMirand
Kricker constructed a knot invariant Z^rat valued in a space of Feynman diagrams with beads. When composed with the "hair" map H, it gives the Kontsevich integral of the knot. We introduce a new grading on diagrams with beads and use it to show that a nontrivial element constructed from Vogel's zero divisor in the algebra Lambda is in the kernel of H. This shows that H is not injective.
(10) Bounded orbits and global fixed points for groups acting on the plane by Kathryn Mann
Let G be a group acting on the plane by orientationpreserving homeomorphisms. We show that a tight bound on orbits implies a global fixed point. Precisely, if for some k>0 there is a ball of radius r > (1/sqrt{3})k such that each point x in the ball satisfies g(x)  h(x)<=k for all g, h in G, and the action of G satisfies a nonwandering hypothesis, then the action has a global fixed point. In particular any group of measurepreserving, orientationpreserving homeomorphisms of the plane with uniformly bounded orbits has a global fixed point. The constant (1/sqrt{3})k is sharp.
As an application, we also show that a group acting on the plane by diffeomorphisms with orbits bounded as above is left orderable.
(11) LusternikSchnirelmann category and the connectivity of X by Nicholas A Scoville
We define and study a homotopy invariant called the connectivity weight to compute the weighted length between spaces X and Y. This is an invariant based on the connectivity of A_i, where A_i is a space attached in a mapping cone sequence from X to Y. We use the LusternikSchnirelmann category to prove a theorem concerning the connectivity of all spaces attached in any decomposition from X to Y. This theorem is used to prove that for any positive rational number q, there is a space X such that q=cl^{omega}(X), the connectivity weighted conelength of X. We compute cl^{omega}(X) and kl^{omega}(X) for many spaces and give several examples.
(12) Some bounds for the knot Floer auinvariant of satellite knots by Lawrence P Roberts
This paper uses four dimensional handlebody theory to compute upper and lower bounds for the Heegaard Floer tauinvariant of almost all satellite knots in terms of the tauinvariants of the pattern and the companion.
(13) Associahedra and weak monoidal structures on categories by Zbigniew Fiedorowicz, Steven Gubkin and Rainer M Vogt
This paper answers the following question: what algebraic structure on a category corresponds to an A_n structure (in the sense of Stasheff) on the geometric realization of its nerve?
(14) A cohomological characterisation of Yu's property A for metric spaces by Jacek Brodzki, Graham A Niblo and Nick Wright
We develop a new framework for cohomology of discrete metric spaces and groups which simultaneously generalises group cohomology, Roe's coarse cohomology, Gersten's \ell^\inftycohomology and Johnson's bounded cohomology. In this framework we give an answer to Higson's question concerning the existence of a cohomological characterisation of Yu's property A, analogous to Johnson's characterisation of amenability. In particular, we introduce an analogue of invariant mean for metric spaces with property A. As an application we extend Guentner's result that box spaces of a finitely generated group have property A if and only if the group is amenable. This provides an alternative proof of Nowak's result that the infinite dimensional cube does not have property A.
(15) Chow rings and decomposition theorems for families of K!3 surfaces and CalabiYau hypersurfaces by Claire Voisin
The decomposition theorem for smooth projective morphisms pi: X>B says that Rpi_*Q decomposes as a direct sum of R^i pi_*Q[i]. We describe simple examples where it is not possible to have such a decomposition compatible with cup product, even after restriction to Zariski dense open sets of B. We prove however that this is always possible for families of K3 surfaces (after shrinking the base), and show how this result relates to a result by Beauville and the author [J. Algebraic Geom. 13 (2004) 417426] on the Chow ring of a K3 surface S. We give two proofs of this result, the first one involving Kautocorrespondences of K3 surfaces, seen as analogues of isogenies of abelian varieties, the second one involving a certain decomposition of the small diagonal in S^3 obtained by Beauville and the author. We also prove an analogue of such a decomposition of the small diagonal in X^3 for CalabiYau hypersurfaces X in P^n, which in turn provides strong restrictions on their Chow ring.
Geometry & Topology Publications is an imprint of Mathematical Sciences Publishers



