Five papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 10 (2010) 315-342
An involution on the K-theory of bimonoidal categories with anti-involution
by Birgit Richter
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p010.xhtml
DOI: 10.2140/agt.2010.10.315
(2) Algebraic & Geometric Topology 10 (2010) 343-372
Cross curvature flow on a negatively curved solid torus
by Jason DeBlois, Dan Knopf and Andrea Young
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p011.xhtml
DOI: 10.2140/agt.2010.10.343
(3) Algebraic & Geometric Topology 10 (2010) 373-432
Stable concordance of knots in 3-manifolds
by Rob Schneiderman
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p012.xhtml
DOI: 10.2140/agt.2010.10.373
(4) Algebraic & Geometric Topology 10 (2010) 433-463
Tangent cones and local geometry of the representation
and character varieties of knot groups
by Leila Ben Abdelghani
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p013.xhtml
DOI: 10.2140/agt.2010.10.433
(5) Algebraic & Geometric Topology 10 (2010) 465-524
Dehn twists in Heegaard Floer homology
by Bijan Sahamie
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p014.xhtml
DOI: 10.2140/agt.2010.10.465
Five papers have been published by Geometry & Topology
(6) Geometry & Topology 14 (2010) 627-718
An open string analogue of Viterbo functoriality
by Mohammed Abouzaid and Paul Seidel
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p015.xhtml
DOI: 10.2140/gt.2010.14.627
(7) Geometry & Topology 14 (2010) 719-754
Some remarks on the size of tubular neighborhoods
in contact topology and fillability
by Klaus Niederkrueger and Francisco Presas
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p016.xhtml
DOI: 10.2140/gt.2010.14.719
(8) Geometry & Topology 14 (2010) 755-772
Homology operations in the topological cyclic homology of a point
by Hakon Schad Bergsaker and John Rognes
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p017.xhtml
DOI: 10.2140/gt.2010.14.755
(9) Geometry & Topology 14 (2010) 773-798
Quasisymmetric nonparametrization and spaces associated
with the Whitehead continuum
by Juha Heinonen and Jang-Mei Wu
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p018.xhtml
DOI: 10.2140/gt.2010.14.773
(10) Geometry & Topology 14 (2010) 799-831
Hausdorff dimension and the Weil-Petersson extension to quasifuchsian space
by Martin Bridgeman
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p019.xhtml
DOI: 10.2140/gt.2010.14.799
Abstracts follow
(1) An involution on the K-theory of bimonoidal categories with anti-involution
by Birgit Richter
We construct a combinatorially defined involution on the algebraic
K-theory of the ring spectrum associated to a bimonoidal category with
anti-involution. Particular examples of such are braided bimonoidal
categories. We investigate examples such as K(ku), K(ko) and
Waldhausen's A-theory of spaces of the form BBG, for abelian groups
G. We show that the involution agrees with the classical one for a
bimonoidal category associated to a ring and prove that it is not
trivial in the above mentioned examples.
(2) Cross curvature flow on a negatively curved solid torus
by Jason DeBlois, Dan Knopf and Andrea Young
The classic 2 pi-Theorem of Gromov and Thurston constructs a
negatively curved metric on certain 3-manifolds obtained by Dehn
filling. By Geometrization, any such manifold admits a hyperbolic
metric. We outline a program using cross curvature flow to construct a
smooth one-parameter family of metrics between the "2 pi-metric" and
the hyperbolic metric. We make partial progress in the program,
proving long-time existence, preservation of negative sectional
curvature, curvature bounds and integral convergence to hyperbolic for
the metrics under consideration.
(3) Stable concordance of knots in 3-manifolds
by Rob Schneiderman
Knots and links in 3-manifolds are studied by applying intersection
invariants to singular concordances. The resulting link invariants
generalize the Arf invariant, the mod 2 Sato--Levine invariants and
Milnor's triple linking numbers. Besides fitting into a general
theory of Whitney towers, these invariants provide obstructions to the
existence of a singular concordance which can be homotoped to an
embedding after stabilization by connected sums with S^2 x
S^2. Results include classifications of stably slice links in
orientable 3-manifolds, stable knot concordance in products of an
orientable surface with the circle and stable link concordance for
many links of null-homotopic knots in orientable 3-manifolds.
(4) Tangent cones and local geometry of the representation
and character varieties of knot groups
by Leila Ben Abdelghani
Let K be a knot in the 3-sphere. We calculate explicitly
the tangent cone to the representation variety at an abelian
representation which corresponds to a double root of the
Alexander polynomial. We also describe the local structure of the
representation and character varieties.
(5) Dehn twists in Heegaard Floer homology
by Bijan Sahamie
We derive a new exact sequence in the hat-version of Heegaard Floer
homology. As a consequence we see a functorial connection between the
invariant of Legendrian knots hat-L and the contact element. As an
application we derive two vanishing results of the contact element
making it possible to easily read off its vanishing out of a surgery
presentation in suitable situations.
(6) An open string analogue of Viterbo functoriality
by Mohammed Abouzaid and Paul Seidel
Liouville domains are a special type of symplectic manifolds with
boundary (they have an everywhere defined Liouville flow, pointing
outwards along the boundary). Symplectic cohomology for Liouville
domains was introduced by Cieliebak-Floer-Hofer-Wysocki and
Viterbo. The latter constructed a restriction (or transfer) map
associated to an embedding of one Liouville domain into another.
In this preprint, we look at exact Lagrangian submanifolds with
Legendrian boundary inside a Liouville domain. The analogue of
symplectic cohomology for such submanifolds is called "wrapped Floer
cohomology". We construct an A_infty-structure on the underlying
wrapped Floer complex, and (under suitable assumptions) an
A_infty-homomorphism realizing the restriction to a Liouville
subdomain. The construction of the A_infty-structure relies on an
implementation of homotopy direct limits, and involves some new moduli
spaces which are solutions of generalized continuation map equations.
(7) Some remarks on the size of tubular neighborhoods
in contact topology and fillability
by Klaus Niederkrueger and Francisco Presas
The well-known tubular neighborhood theorem for contact submanifolds
states that a small enough neighborhood of such a submanifold N is
uniquely determined by the contact structure on N, and the conformal
symplectic structure of the normal bundle. In particular, if the
submanifold N has trivial normal bundle then its tubular neighborhood
will be contactomorphic to a neighborhood of N x {0} in the model
space N x R^2k.
In this article we make the observation that if (N,xi_N) is a
3-dimensional overtwisted submanifold with trivial normal bundle in
(M,xi), and if its model neighborhood is sufficiently large, then
(M,xi) does not admit a symplectically aspherical filling.
(8) Homology operations in the topological cyclic homology of a point
by Hakon Schad Bergsaker and John Rognes
We consider the commutative S-algebra given by the topological cyclic
homology of a point. The induced Dyer-Lashof operations in mod p
homology are shown to be nontrivial for p=2, and an explicit formula
is given. As a part of the calculation, we are led to compare the
fixed point spectrum S^G of the sphere spectrum and the algebraic
K-theory spectrum of finite G-sets, as structured ring spectra.
(9) Quasisymmetric nonparametrization and spaces
associated with the Whitehead continuum
by Juha Heinonen and Jang-Mei Wu
The decomposition space R^3/Wh associated with the Whitehead continuum
Wh is not a manifold, but the product (R^3/Wh) x R^m is homeomorphic
to R^{3+m} for any m >= 1 (known since the 1960's). We study the
quasisymmetric structure on (R^3/Wh) x R^m and show that the space
(R^3/Wh) x R^m may be equipped with a metric resembling R^{3+m}
geometrically and measure theoretically - it is linearly locally
contractible and Ahlfors (3+m)-regular - nevertheless the resulting
space does not admit a quasisymmetric parametrization by R^{3+m}.
(10) Hausdorff dimension and the Weil-Petersson extension to
quasifuchsian space
by Martin Bridgeman
We consider a natural nonnegative two-form G on quasifuchsian space
that extends the Weil-Petersson metric on Teichmueller space. We
describe completely the positive definite locus of G, showing that it
is a positive definite metric off the fuchsian diagonal of
quasifuchsian space and is only zero on the "pure-bending" tangent
vectors to the fuchsian diagonal. We show that G is equal to the
pullback of the pressure metric from dynamics. We use the properties
of G to prove that at any critical point of the Hausdorff dimension
function on quasifuchsian space the Hessian of the Hausdorff dimension
function must be positive definite on at least a half-dimensional
subspace of the tangent space. In particular this implies that
Hausdorff dimension has no local maxima on quasifuchsian space.
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