5,333 research outputs found
Knotted Legendrian surfaces with few Reeb chords
For , we construct Legendrian embeddings of a surface of genus
into which lie in pairwise distinct Legendrian isotopy classes
and which all have transverse Reeb chords ( is the conjecturally
minimal number of chords). Furthermore, for of the embeddings the
Legendrian contact homology DGA does not admit any augmentation over ,
and hence cannot be linearized. We also investigate these surfaces from the
point of view of the theory of generating families. Finally, we consider
Legendrian spheres and planes in from a similar perspective.Comment: 30 pages, 11 figure
Effect of Legendrian Surgery
The paper is a summary of the results of the authors concerning computations
of symplectic invariants of Weinstein manifolds and contains some examples and
applications. Proofs are sketched. The detailed proofs will appear in our
forthcoming paper. In the Appendix written by S. Ganatra and M. Maydanskiy it
is shown that the results of this paper imply P. Seidel's conjecture equating
symplectic homology with Hochschild homology of a certain Fukaya category.Comment: v.4 is significantly extended, especially Sections 6 and 8. Several
other sections, including Appendix are rewritte
Filtrations on the knot contact homology of transverse knots
We construct a new invariant of transverse links in the standard contact
structure on R^3. This invariant is a doubly filtered version of the knot
contact homology differential graded algebra (DGA) of the link. Here the knot
contact homology of a link in R^3 is the Legendrian contact homology DGA of its
conormal lift into the unit cotangent bundle S^*R^3 of R^3, and the filtrations
are constructed by counting intersections of the holomorphic disks of the DGA
differential with two conormal lifts of the contact structure. We also present
a combinatorial formula for the filtered DGA in terms of braid representatives
of transverse links and apply it to show that the new invariant is independent
of previously known invariants of transverse links.Comment: 23 pages, v2: minor corrections suggested by refere
Agricultural phosphorus losses and eutrophication in Nordic-Baltic countries
The P losses from agriculture are controlled by natural characteristics, agricultural practices and national and international agricultural as well as agri-environmental policies. To reduce the P losses the measures should be targeted at the areas and activities that are responsible for the highest actual losses of bioavailable P. The response of an aquatic ecosystem to agricultural activities is a result of complex interactions between physical, chemical and biological processes
Regular homotopy and total curvature
We consider properties of the total absolute geodesic curvature functional on
circle immersions into a Riemann surface. In particular, we study its behavior
under regular homotopies, its infima in regular homotopy classes, and the
homotopy types of spaces of its local minima.
We consider properties of the total curvature functional on the space of
2-sphere immersions into 3-space. We show that the infimum over all sphere
eversions of the maximum of the total curvature during an eversion is at most
8\pi and we establish a non-injectivity result for local minima.Comment: This is the version published by Algebraic & Geometric Topology on 23
March 2006. arXiv admin note: this version concatenates two articles
published in Algebraic & Geometric Topolog
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