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Ten papers published by Geometry & Topology Publications
Posted:
May 7, 2012 8:56 AM


Seven papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 12 (2012) 933950 Free group automorphisms with parabolic boundary orbits by Arnaud Hilion URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p033.xhtml DOI: 10.2140/agt.2012.12.933
(2) Algebraic & Geometric Topology 12 (2012) 951961 Products of Greek letter elements dug up from the third Morava stabilizer algebra by Ryo Kato and Katsumi Shimomura URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p034.xhtml DOI: 10.2140/agt.2012.12.951
(3) Algebraic & Geometric Topology 12 (2012) 963977 Concordance to links with unknotted components by Jae Choon Cha and Daniel Ruberman URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p035.xhtml DOI: 10.2140/agt.2012.12.963
(4) Algebraic & Geometric Topology 12 (2012) 979995 Random groups arising as graph products by Ruth Charney and Michael Farber URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p036.xhtml DOI: 10.2140/agt.2012.12.979
(5) Algebraic & Geometric Topology 12 (2012) 9971057 On the universal sl_2 invariant of boundary bottom tangles by Sakie Suzuki URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p037.xhtml DOI: 10.2140/agt.2012.12.997
(6) Algebraic & Geometric Topology 12 (2012) 10591079 Inequivalent handlebodyknots with homeomorphic complements by Jung Hoon Lee and Sangyop Lee URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p038.xhtml DOI: 10.2140/agt.2012.12.1059
(7) Algebraic & Geometric Topology 12 (2012) 10811098 The link concordance invariant from Lee homology by John Pardon URL: http://www.msp.warwick.ac.uk/agt/2012/1202/p039.xhtml DOI: 10.2140/agt.2012.12.1081
Three papers have been published by Geometry & Topology
(8) Geometry & Topology 16 (2012) 665683 Oneended subgroups of graphs of free groups with cyclic edge groups by Henry Wilton URL: http://www.msp.warwick.ac.uk/gt/2012/1602/p014.xhtml DOI: 10.2140/gt.2012.16.665
(9) Geometry & Topology 16 (2012) 685750 On the Taylor tower of relative Ktheory by Ayelet Lindenstrauss and Randy McCarthy URL: http://www.msp.warwick.ac.uk/gt/2012/1602/p015.xhtml DOI: 10.2140/gt.2012.16.685
(10) Geometry & Topology 16 (2012) 751779 Monopole Floer homology and Legendrian knots by Steven Sivek URL: http://www.msp.warwick.ac.uk/gt/2012/1602/p016.xhtml DOI: 10.2140/gt.2012.16.751
Abstracts follow
(1) Free group automorphisms with parabolic boundary orbits by Arnaud Hilion
For N at least 4, we show that there exist automorphisms of the free group F_n which have a parabolic orbit in its boundary. In fact, we exhibit a technology for producing infinitely many such examples.
(2) Products of Greek letter elements dug up from the third Morava stabilizer algebra by Ryo Kato and Katsumi Shimomura
In [Hiroshima Math. J. 12 (1982) 611626], Oka and the second author considered the cohomology of the second Morava stabilizer algebra to study nontriviality of the products of beta elements of the stable homotopy groups of spheres. In this paper, we use the cohomology of the third Morava stabilizer algebra to find nontrivial products of Greek letters of the stable homotopy groups of spheres: alpha_1*gamma_t, beta_2*gamma_t, <alpha_1,alpha_1,beta_{p/p}^p>*gamma_t*beta_1 and <beta_1,p,gamma_t> for t with p not dividing t(t^21) for a prime number p>5.
(3) Concordance to links with unknotted components by Jae Choon Cha and Daniel Ruberman
We show that there are topologically slice links whose individual components are smoothly concordant to the unknot, but which are not smoothly concordant to any link with unknotted components. We also give generalizations in the topological category regarding components of prescribed Alexander polynomials. The main tools are covering link calculus, algebraic invariants of rational knot concordance theory, and the correction term of Heegaard Floer homology.
(4) Random groups arising as graph products by Ruth Charney and Michael Farber
In this paper we study the hyperbolicity properties of a class of random groups arising as graph products associated to random graphs. Recall, that the construction of a graph product is a generalization of the constructions of rightangled Artin and Coxeter groups. We adopt the Erdos and Renyi model of a random graph and find precise threshold functions for hyperbolicity (or relative hyperbolicity). We also study automorphism groups of rightangled Artin groups associated to random graphs. We show that with probability tending to one as n > infinity, random rightangled Artin groups have finite outer automorphism groups, assuming that the probability parameter p is constant and satisfies 0.2929<p<1.
(5) On the universal sl_2 invariant of boundary bottom tangles by Sakie Suzuki
The universal sl_2 invariant of bottom tangles has a universality property for the colored Jones polynomial of links. A bottom tangle is called boundary if its components admit mutually disjoint Seifert surfaces. Habiro conjectured that the universal sl_2 invariant of boundary bottom tangles takes values in certain subalgebras of the completed tensor powers of the quantized enveloping algebra U_h(sl_2) of the Lie algebra sl_2. In the present paper, we prove an improved version of Habiro's conjecture. As an application, we prove a divisibility property of the colored Jones polynomial of boundary links.
(6) Inequivalent handlebodyknots with homeomorphic complements by Jung Hoon Lee and Sangyop Lee
We distinguish the handlebodyknots 5_1, 6_4 and 5_2, 6_{13} in the table, due to Ishii et al, of irreducible handlebodyknots up to six crossings. Furthermore, we construct two infinite families of handlebodyknots, each containing one of the pairs 5_1, 6_4 and 5_2, 6_{13}, and show that any two handlebodyknots in each family have homeomorphic complements but they are not equivalent.
(7) The link concordance invariant from Lee homology by John Pardon
We use the knot homology of Khovanov and Lee to construct link concordance invariants generalizing the Rasmussen sinvariant of knots. The relevant invariant for a link is a filtration on a vector space of dimension 2^L. The basic properties of the sinvariant all extend to the case of links; in particular, any orientable cobordism Sigma between links induces a map between their corresponding vector spaces which is filtered of degree chi(Sigma). A corollary of this construction is that any componentpreserving orientable cobordism from a Khthin link to a link split into k components must have genus at least the floor of k/2. In particular, no quasialternating link is concordant to a split link.
(8) Oneended subgroups of graphs of free groups with cyclic edge groups by Henry Wilton Consider a oneended wordhyperbolic group. If it is the fundamental group of a graph of free groups with cyclic edge groups then either it is the fundamental group of a surface or it contains a finitely generated oneended subgroup of infinite index. As a corollary, the same holds for limit groups. We also obtain a characterisation of surfaces with boundary among free groups equipped with peripheral structures.
(9) On the Taylor tower of relative Ktheory by Ayelet Lindenstrauss and Randy McCarthy
For R a discrete ring, M a simplicial Rbimodule, and X a simplicial set, we construct the Goodwillie Taylor tower of the reduced $K$theory of parametrized endomorphisms tilde K(R;tilde M[X]) as a functor of X. Resolving general Rbimodules by bimodules of the form tilde M[X], this also determines the Goodwillie Taylor tower of tilde K(R; M) as a functor of M. The towers converge when X or M is connected. This also gives the Goodwillie Taylor tower of tilde K(R semix M) ~= tilde K(R;B.M) as a functor of M.
For a functor with smash product F and an Fbimodule P, we construct an invariant W(F;P) which is an analog of TR(F) with coefficients. We study the structure of this invariant and its finitestage approximations W_n(F;P) and conclude that the functor sending X to W_n(R;tilde M[X]) is the $n$th stage of the Goodwillie calculus Taylor tower of the functor which sends X to tilde K(R; tilde M[X]). Thus the functor sending X to W(R;tilde M[X]) is the full Taylor tower, which converges to tilde K(R;tilde M[X]) for connected X.
(10) Monopole Floer homology and Legendrian knots by Steven Sivek
We use monopole Floer homology for sutured manifolds to construct invariants of unoriented Legendrian knots in a contact 3manifold. These invariants assign to a knot K in Y elements of the monopole knot homology KHM(Y,K), and they strongly resemble the knot Floer homology invariants of Lisca, Ozsvath, Stipsicz, and Szabo. We prove several vanishing results, investigate their behavior under contact surgeries, and use this to construct many examples of nonloose knots in overtwisted 3manifolds. We also show that these invariants are functorial with respect to Lagrangian concordance.
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