Eight papers and an erratum published by Geometry & Topology Publications
Geometry and Topology
(1) Algebraic & Geometric Topology 10 (2010) 825-836
Ozsvath-Szabo and Rasmussen invariants of cable knots
by Cornelia A Van Cott
URL: http://www.msp.warwick.ac.uk/agt/2010/10-02/p026.xhtml
DOI: 10.2140/agt.2010.10.825
(2) Algebraic & Geometric Topology 10 (2010) 837-851
Infinite generation of the kernels of the Magnus and Burau
representations
by Thomas Church and Benson Farb
URL: http://www.msp.warwick.ac.uk/agt/2010/10-02/p027.xhtml
DOI: 10.2140/agt.2010.10.837
(3) Algebraic & Geometric Topology 10 (2010) 853-865
Triple point numbers of surface-links and symmetric quandle
cocycle invariants
by Kanako Oshiro
URL: http://www.msp.warwick.ac.uk/agt/2010/10-02/p028.xhtml
DOI: 10.2140/agt.2010.10.853
(4) Algebraic & Geometric Topology 10 (2010) 867-890
Degree +/-1 self-maps and self-homeomorphisms on prime 3-manifolds
by Hongbin Sun
URL: http://www.msp.warwick.ac.uk/agt/2010/10-02/p029.xhtml
DOI: 10.2140/agt.2010.10.867
(5) Algebraic & Geometric Topology 10 (2010) 891-916
Studying uniform thickness I: Legendrian simple iterated torus knots
by Douglas J LaFountain
URL: http://www.msp.warwick.ac.uk/agt/2010/10-02/p030.xhtml
DOI: 10.2140/agt.2010.10.891
Three papers have been published by Geometry & Topology
(6) Geometry & Topology 14 (2010) 1063-1094
Asymptotic geometry in products of Hadamard spaces with rank one isometries
by Gabriele Link
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p024.xhtml
DOI: 10.2140/gt.2010.14.1063
(7) Geometry & Topology 14 (2010) 1095-1110
A local curvature bound in Ricci flow
by Peng Lu
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p025.xhtml
DOI: 10.2140/gt.2010.14.1095
(8) Geometry & Topology 14 (2010) 1111-1127
Structured ring spectra and displays
by Tyler Lawson
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p026.xhtml
DOI: 10.2140/gt.2010.14.1111
One erratum has been published by Geometry & Topology Monographs
(9) Geometry & Topology Monographs 2 (1999) 577-581
Genus two Heegaard splittings: an omission
by Martin Scharlemann
URL: http://www.msp.warwick.ac.uk/gtm/1999/02/p028.xhtml
DOI: 10.2140/gtm.1999.2.577
Abstracts follow
(1) Ozsvath-Szabo and Rasmussen invariants of cable knots
by Cornelia A Van Cott
We study the behavior of the Ozsvath--Szabo and Rasmussen knot
concordance invariants tau and s on K_{m,n}, the (m,n)-cable of a knot
K where m and n are relatively prime. We show that for every knot K
and for any fixed positive integer m, both of the invariants evaluated
on K_{m,n} differ from their value on the torus knot T_{m,n} by fixed
constants for all but finitely many n>0. Combining this result
together with Hedden's extensive work on the behavior of tau on
(m,mr+1)-cables yields bounds on the value of tau on any (m,n)-cable
of K. In addition, several of Hedden's obstructions for cables
bounding complex curves are extended.
(2) Infinite generation of the kernels of the Magnus and Burau
representations
by Thomas Church and Benson Farb
Consider the kernel Mag_g of the Magnus representation of the Torelli
group and the kernel Bur_n of the Burau representation of the braid
group. We prove that for g >= 2 and for n >= 6 the groups Mag_g and
Bur_n have infinite rank first homology. As a consequence we conclude
that neither group has any finite generating set. The method of proof
in each case consists of producing a kind of "Johnson-type"
homomorphism to an infinite rank abelian group, and proving the image
has infinite rank. For the case of Bur_n, we do this with the
assistance of a computer calculation.
(3) Triple point numbers of surface-links and symmetric quandle
cocycle invariants
by Kanako Oshiro
For any positive integer n, we give a 2-component surface-link
F = F_1 \cup F_2 such that F_1 is orientable, F_2 is non-orientable
and the triple point number of F is equal to 2n. To give lower bounds
of the triple point numbers, we use symmetric quandle cocycle invariants.
(4) Degree +/-1 self-maps and self-homeomorphisms on prime 3-manifolds
by Hongbin Sun
We determine all closed orientable geometrizable prime 3-manifolds
that admit a degree 1 or -1 self-map not homotopic to a homeomorphism.
(5) Studying uniform thickness I: Legendrian simple iterated torus knots
by Douglas J LaFountain
We prove that the class of topological knot types that are both
Legendrian simple and satisfy the uniform thickness property (UTP) is
closed under cabling. An immediate application is that all iterated
cabling knot types that begin with negative torus knots are Legendrian
simple. We also examine, for arbitrary numbers of iterations,
iterated cablings that begin with positive torus knots, and establish
the Legendrian simplicity of large classes of these knot types, many
of which also satisfy the UTP. In so doing we obtain new necessary
conditions for both the failure of the UTP and Legendrian
nonsimplicity in the class of iterated torus knots, including specific
conditions on knot types.
(6) Asymptotic geometry in products of Hadamard spaces with rank one isometries
by Gabriele Link
In this article we study asymptotic properties of certain discrete
groups Gamma acting by isometries on a product X=X_1 times X_2 of
locally compact Hadamard spaces which admit a geodesic without flat
half-plane. The motivation comes from the fact that Kac--Moody groups
over finite fields, which can be seen as generalizations of arithmetic
groups over function fields, belong to the considered class of
groups. Hence one may ask whether classical properties of discrete
subgroups of higher rank Lie groups as in Benoist [Geom. Funct. Anal.
7 (1997) 1-47] and Quint [Comment. Math. Helv. 77 (2002) 563-608]
hold in this context.
In the first part of the paper we describe the structure of the
geometric limit set of Gamma and prove statements analogous to the
results of Benoist. The second part is concerned with the exponential
growth rate delta_theta(Gamma) of orbit points in X with a prescribed
"slope" theta ranging in (0,pi/2), which appropriately generalizes the
critical exponent in higher rank. In analogy to Quint's result we
show that the homogeneous extension Psi_Gamma to R_{>=0}^2 of
delta_theta(Gamma) as a function of theta is upper semicontinuous and
concave.
(7) A local curvature bound in Ricci flow
by Peng Lu
In this note we give a proof of a result which is closely related to Perelman's
theorem in Section 10.3 of the paper "The entropy formula for the Ricci flow
and its geometric applications" [arXiv:math.DG/0211159].
(8) Structured ring spectra and displays
by Tyler Lawson
We combine Lurie's generalization of the Hopkins-Miller theorem with
work of Zink-Lau on displays to give a functorial construction of
even-periodic E_infty ring spectra E, concentrated in chromatic layers
2 and above, associated to certain n times n invertible matrices with
coefficients in the Witt ring of pi_0(E). This is applied to examples
related to Lubin-Tate and Johnson-Wilson spectra. We also give a
Hopf algebroid presentation of the moduli of p-divisible groups of
height greater than or equal to 2.
(9) Genus two Heegaard splittings: an omission
by Martin Scharlemann
In Rubinstein and Scharlemann [Geom. Topol. Monogr. 2 (1999) 489-553],
the given list of ways in which a closed orientable 3-manifold could
have distinct genus two Heegaard splittings misses a significant case.
A brief description of the case (discovered by John Berge) is given
here, and the proof that the list is complete is corrected, now
incorporating the missed case. Full details and further discussion
appear elsewhere.