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Eleven papers published by GTP completing 2011 publication
Posted:
Dec 26, 2011 11:30 AM


This announcement completes GTP publication for 2011.
Papers (1)(5) complete AGT Volume 11 (2011) and papers (6)(11) complete GT Volume 15 (2011). Publiction in 2012 will commence on January 1 2012. Seasons greetings to all!
Five papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 29412970 Representation spaces of pretzel knots by Raphael Zentner URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p095.xhtml DOI: 10.2140/agt.2011.11.2941
(2) Algebraic & Geometric Topology 11 (2011) 29713010 Reducible braids and Garside Theory by Juan GonzalezMeneses and Bert Wiest URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p096.xhtml DOI: 10.2140/agt.2011.11.2971
(3) Algebraic & Geometric Topology 11 (2011) 30113041 Representation stability for the cohomology of the moduli space M_g^n by Rita Jimenez Rolland URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p097.xhtml DOI: 10.2140/agt.2011.11.3011
(4) Algebraic & Geometric Topology 11 (2011) 30433064 The Fox property for codimension one embeddings of products of three spheres into spheres by Laercio Aparecido Lucas and Osamu Saeki URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p098.xhtml DOI: 10.2140/agt.2011.11.3043
(5) Algebraic & Geometric Topology 11 (2011) 30653084 Constructing free actions of pgroups on products of spheres by Michele Klaus URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p099.xhtml DOI: 10.2140/agt.2011.11.3065
Six papers have been published by Geometry & Topology
(6) Geometry & Topology 15 (2011) 21812233 Strongly contracting geodesics in Outer Space by Yael AlgomKfir URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p054.xhtml DOI: 10.2140/gt.2011.15.2181
(7) Geometry & Topology 15 (2011) 22352273 Rigidity of spherical codes by Henry Cohn, Yang Jiao, Abhinav Kumar and Salvatore Torquato URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p055.xhtml DOI: 10.2140/gt.2011.15.2235
(8) Geometry & Topology 15 (2011) 22752298 On intrinsic geometry of surfaces in normed spaces by Dmitri Burago and Sergei Ivanov URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p056.xhtml DOI: 10.2140/gt.2011.15.2275
(9) Geometry & Topology 15 (2011) 22992319 Rigidity of polyhedral surfaces, III by Feng Luo URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p057.xhtml DOI: 10.2140/gt.2011.15.2299
(10) Geometry & Topology 15 (2011) 23212350 Counting lattice points in compactified moduli spaces of curves by Norman Do and Paul Norbury URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p058.xhtml DOI: 10.2140/gt.2011.15.2321
(11) Geometry & Topology 15 (2011) 23512457 Intersection theory of punctured pseudoholomorphic curves by Richard Siefring URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p059.xhtml DOI: 10.2140/gt.2011.15.2351
Abstracts follow
(1) Representation spaces of pretzel knots by Raphael Zentner
We study the representation spaces R(K;i) appearing in Kronheimer and Mrowka's instanton knot Floer homologies for a class of pretzel knots. In particular, for pretzel knots P(p,q,r) with p, q, r pairwise coprime, these appear to be nondegenerate and comprise representations in SU(2) that are not binary dihedral.
(2) Reducible braids and Garside Theory by Juan GonzalezMeneses and Bert Wiest We show that reducible braids which are, in a Garsidetheoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its conjugacy class which we call the stabilized set of sliding circuits, and if it is reducible, then its reducibility is geometrically obvious: it has a round or almost round reducing curve. Moreover, for any given braid, an element of its stabilized set of sliding circuits can be found using the wellknown cyclic sliding operation. This leads to a polynomial time algorithm for deciding the NielsenThurston type of any braid, modulo one wellknown conjecture on the speed of convergence of the cyclic sliding operation.
(3) Representation stability for the cohomology of the moduli space M_g^n by Rita Jimenez Rolland
Let M_g^n be the moduli space of Riemann surfaces of genus g with n labeled marked points. We prove that, for g >= 2, the cohomology groups {H^i(M_g^n;Q)}_{n=1}^{\infty} form a sequence of S_nrepresentations which is representation stable in the sense of ChurchFarb. In particular this result applied to the trivial S_nrepresentation implies rational "puncture homological stability" for the mapping class group Mod_g^n. We obtain representation stability for sequences {H^i(PMod^n(M);Q)}_{n=1}^{\infty}, where PMod^n(M) is the mapping class group of many connected orientable manifolds M of dimension d >= 3 with centerless fundamental group; and for sequences {H^i(BPDiff^n(M);Q)}_{n=1}^{\infty}, where BPDiff^n(M) is the classifying space of the subgroup PDiff^n(M) of diffeomorphisms of M that fix pointwise n distinguished points in M.
(4) The Fox property for codimension one embeddings of products of three spheres into spheres by Laercio Aparecido Lucas and Osamu Saeki
Fox has shown that for every closed connected surface smoothly embedded in S^3, the closure of each component of its complement is diffeomorphic to the closure of the complement of a handlebody embedded in S^3. In this paper, we study a similar `Fox property' for smooth embeddings of S^p x S^q x S^r in S^{p+q+r+1}.
(5) Constructing free actions of pgroups on products of spheres by Michele Klaus
We prove that, for p an odd prime, every finite pgroup of rank 3 acts freely on a finite complex X homotopy equivalent to a product of three spheres.
(6) Strongly contracting geodesics in Outer Space by Yael AlgomKfir
We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(F_n) are Morse, meaning that a quasigeodesic with endpoints on the axis stays within a bounded distance from the axis.
(7) Rigidity of spherical codes by Henry Cohn, Yang Jiao, Abhinav Kumar and Salvatore Torquato
A packing of spherical caps on the surface of a sphere (that is, a spherical code) is called rigid or jammed if it is isolated within the space of packings. In other words, aside from applying a global isometry, the packing cannot be deformed. In this paper, we systematically study the rigidity of spherical codes, particularly kissing configurations. One surprise is that the kissing configuration of the CoxeterTodd lattice is not jammed, despite being locally jammed (each individual cap is held in place if its neighbors are fixed); in this respect, the CoxeterTodd lattice is analogous to the facecentered cubic lattice in three dimensions. By contrast, we find that many other packings have jammed kissing configurations, including the BarnesWall lattice and all of the best kissing configurations known in four through twelve dimensions. Jamming seems to become much less common for large kissing configurations in higher dimensions, and in particular it fails for the best kissing configurations known in 25 through 31 dimensions. Motivated by this phenomenon, we find new kissing configurations in these dimensions, which improve on the records set in 1982 by the laminated lattices.
(8) On intrinsic geometry of surfaces in normed spaces by Dmitri Burago and Sergei Ivanov
We prove three facts about intrinsic geometry of surfaces in a normed (Minkowski) space. When put together, these facts demonstrate a rather intriguing picture. We show that (1) geodesics on saddle surfaces (in a space of any dimension) behave as they are expected to: they have no conjugate points and thus minimize length in their homotopy class; (2) in contrast, every twodimensional Finsler manifold can be locally embedded as a saddle surface in a 4dimensional space; and (3) geodesics on convex surfaces in a 3dimensional space also behave as they are expected to: on a complete strictly convex surface, no complete geodesic minimizes the length globally.
(9) Rigidity of polyhedral surfaces, III by Feng Luo
This paper investigates several global rigidity issues for polyhedral surfaces including inversive distance circle packings. Inversive distance circle packings are polyhedral surfaces introduced by P Bowers and K Stephenson in [Mem. Amer. Math. Soc. 170, no. 805, Amer. Math. Soc. (2004)] as a generalization of Andreev and Thurston's circle packing. They conjectured that inversive distance circle packings are rigid. We prove this conjecture using recent work of R Guo [Trans. Amer. Math. Soc. 363 (2011) 47574776] on the variational principle associated to the inversive distance circle packing. We also show that each polyhedral metric on a triangulated surface is determined by various discrete curvatures that we introduced in [arXiv 0612.5714], verifying a conjecture in [arXiv 0612.5714]. As a consequence, we show that the discrete Laplacian operator determines a spherical polyhedral metric.
(10) Counting lattice points in compactified moduli spaces of curves by Norman Do and Paul Norbury
We define and count lattice points in the moduli space bar{M}_{g,n} of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified moduli space M_{g,n}. The enumeration produces polynomials whose top degree coefficients are tautological intersection numbers on bar{M}_{g,n} and whose constant term is the orbifold Euler characteristic of bar{M}_{g,n}. We prove a recursive formula which can be used to effectively calculate these polynomials. One consequence of these results is a simple recursion relation for the orbifold Euler characteristic of bar{M}_{g,n}.
(11) Intersection theory of punctured pseudoholomorphic curves by Richard Siefring We study the intersection theory of punctured pseudoholomorphic curves in 4dimensional symplectic cobordisms. Using the asymptotic results of the author [Comm. Pure Appl. Math. 61(2008) 163184], we first study the local intersection properties of such curves at the punctures. We then use this to develop topological controls on the intersection number of two curves. We also prove an adjunction formula which gives a topological condition that will guarantee a curve in a given homotopy class is embedded, extending previous work of Hutchings [JEMS 4(2002) 31361].
We then turn our attention to curves in the symplectization R x M of a 3manifold M admitting a stable Hamiltonian structure. We investigate controls on intersections of the projections of curves to the 3manifold and we present conditions that will guarantee the projection of a curve to the 3manifold is an embedding.
Finally we consider an application concerning pseudoholomorphic curves in manifolds admitting a certain class of holomorphic open book decomposition and an application concerning the existence of generalized pseudoholomorphic curves, as introduced by Hofer [Geom. Func. Anal. (2000) 674704] .
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