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Ten papers published by Geometry & Topology Publications
Posted:
May 7, 2012 8:56 AM
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Seven papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 12 (2012) 933-950
Free group automorphisms with parabolic boundary orbits
by Arnaud Hilion
URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p033.xhtml
DOI: 10.2140/agt.2012.12.933
(2) Algebraic & Geometric Topology 12 (2012) 951-961
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/2012/12-02/p034.xhtml
DOI: 10.2140/agt.2012.12.951
(3) Algebraic & Geometric Topology 12 (2012) 963-977
Concordance to links with unknotted components
by Jae Choon Cha and Daniel Ruberman
URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p035.xhtml
DOI: 10.2140/agt.2012.12.963
(4) Algebraic & Geometric Topology 12 (2012) 979-995
Random groups arising as graph products
by Ruth Charney and Michael Farber
URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p036.xhtml
DOI: 10.2140/agt.2012.12.979
(5) Algebraic & Geometric Topology 12 (2012) 997-1057
On the universal sl_2 invariant of boundary bottom tangles
by Sakie Suzuki
URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p037.xhtml
DOI: 10.2140/agt.2012.12.997
(6) Algebraic & Geometric Topology 12 (2012) 1059-1079
Inequivalent handlebody-knots with homeomorphic complements
by Jung Hoon Lee and Sangyop Lee
URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p038.xhtml
DOI: 10.2140/agt.2012.12.1059
(7) Algebraic & Geometric Topology 12 (2012) 1081-1098
The link concordance invariant from Lee homology
by John Pardon
URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p039.xhtml
DOI: 10.2140/agt.2012.12.1081
Three papers have been published by Geometry & Topology
(8) Geometry & Topology 16 (2012) 665-683
One-ended subgroups of graphs of free groups with cyclic edge groups
by Henry Wilton
URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/p014.xhtml
DOI: 10.2140/gt.2012.16.665
(9) Geometry & Topology 16 (2012) 685-750
On the Taylor tower of relative K-theory
by Ayelet Lindenstrauss and Randy McCarthy
URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/p015.xhtml
DOI: 10.2140/gt.2012.16.685
(10) Geometry & Topology 16 (2012) 751-779
Monopole Floer homology and Legendrian knots
by Steven Sivek
URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/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) 611--626], 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^2-1) 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 right-angled 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 right-angled
Artin groups associated to random graphs. We show that with
probability tending to one as n --> infinity, random right-angled
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 handlebody-knots with homeomorphic complements
by Jung Hoon Lee and Sangyop Lee
We distinguish the handlebody-knots 5_1, 6_4 and 5_2, 6_{13} in the
table, due to Ishii et al, of irreducible handlebody-knots up to six
crossings. Furthermore, we construct two infinite families of
handlebody-knots, each containing one of the pairs 5_1, 6_4 and 5_2,
6_{13}, and show that any two handlebody-knots 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 s-invariant of
knots. The relevant invariant for a link is a filtration on a vector
space of dimension 2^|L|. The basic properties of the s-invariant 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 component-preserving orientable cobordism
from a Kh-thin link to a link split into k components must have genus
at least the floor of k/2. In particular, no quasi-alternating link
is concordant to a split link.
(8) One-ended subgroups of graphs of free groups with cyclic edge groups
by Henry Wilton
Consider a one-ended word-hyperbolic 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 one-ended 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 K-theory
by Ayelet Lindenstrauss and Randy McCarthy
For R a discrete ring, M a simplicial R-bimodule, 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 R-bimodules 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 semi-x M) ~= tilde K(R;B.M) as a
functor of M.
For a functor with smash product F and an F-bimodule 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 finite-stage 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 3-manifold.
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 3-manifolds. We also show that these invariants are
functorial with respect to Lagrangian concordance.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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