Four papers published by Geometric & Topology Publications
- From: Geometry and Topology <gt@xxxxxxxxxxxxxxxxx>
- Date: Mon, 24 Jul 2006 13:00:12 +0000 (UTC)
Geometry & Topology Publications have published four papers. Two
are published by Geometry & Topology and two by Algebraic & Geometric
Topology.
--
Published by Geometry & Topology at
http://www.maths.warwick.ac.uk/gt/gtcontents10.html
(1) Pseudoholomorphic punctured spheres in R x S^1 x S^2:
Properties and existence
by Clifford Henry Taubes
(2) Global rigidity for totally nonsymplectic Anosov Z^k actions
by Boris Kalinin and Victoria Sadovskaya
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Published by Algebraic & Geometric Topology at
http://www.maths.warwick.ac.uk/agt/agtcontents6.html
(3) Dyer-Lashof-Cohen operations in Hochschild cohomology
by Victor Tourtchine
(4) Generating family invariants for Legendrian links of unknots
by Jill Jordan and Lisa Traynor
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Abstracts and URL's follow:
(1) Pseudoholomorphic punctured spheres in R x S^1 x S^2:
Properties and existence
by Clifford Henry Taubes
http://msp.warwick.ac.uk/gt/ftp/main/2006/gt-10-23.pdf
This is the first of at least two articles that describe the moduli
spaces of pseudoholomorphic, multiply punctured spheres in R x (S^1 x
S^2) as defined by a certain natural pair of almost complex structure
and symplectic form. This article proves that all moduli space
components are smooth manifolds. Necessary and sufficient conditions
are also given for a collection of closed curves in S^1 x S^2
to appear as the set of |s| --> infinity limits of the constant s in R
slices of a pseudoholomorphic, multiply punctured sphere.
(2) Global rigidity for totally nonsymplectic Anosov Z^k actions
by Boris Kalinin and Victoria Sadovskaya
http://msp.warwick.ac.uk/gt/ftp/main/2006/gt-10-24.pdf
We consider a totally nonsymplectic Anosov action of Z^k
which is either uniformly quasiconformal or pinched on each coarse
Lyapunov distribution. We show that such an action on a torus is
C^\infty--conjugate to an action by affine automorphisms. We also
obtain similar global rigidity results for actions on an arbitrary
compact manifold assuming that the coarse Lyapunov foliations are
jointly integrable.
(3) Dyer-Lashof-Cohen operations in Hochschild cohomology
by Victor Tourtchine
http://msp.warwick.ac.uk/agt/ftp/main/2006/agt-06-33.pdf
We give explicit formulae for operations in Hochschild cohomology which
are analogous to the operations in the homology of double loop spaces.
As a corollary we obtain that any brace algebra in finite characteristic
is always a restricted Lie algebra.
(4) Generating family invariants for Legendrian links of unknots
by Jill Jordan and Lisa Traynor
http://msp.warwick.ac.uk/agt/ftp/main/2006/gt-06-34.pdf
Theory is developed for linear-quadratic at infinity generating families
for Legendrian knots in R^3. It is shown that the unknot
with maximal Thurston--Bennequin invariant of -1 has a unique
linear-quadratic at infinity generating family, up to fiber-preserving
diffeomorphism and stabilization. From this, invariant generating
family polynomials are constructed for 2-component Legendrian links
where each component is a maximal unknot. Techniques are developed to
compute these polynomials, and computations are done for two families
of Legendrian links: rational links and twist links. The polynomials
allow one to show that some topologically equivalent links with the same
classical invariants are not Legendrian equivalent. It is also shown
that for these families of links the generating family polynomials agree
with the polynomials arising from a linearization of the differential
graded algebra associated to the links.
.
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