1,720,973 research outputs found
Duality for Contact Homology of Legendrian knots
No full textIn this paper, I prove a beautiful symmetry property for the contact homology invariant of Legendrian knots, which are mathematical knots that satisfy an additional geometric property. In addition to its intrinsic beauty, the symmetry simplifies calculations; further, the framework developed in its proof opens up further research into the structure of the invariant. --author-supplied descriptio
Obstructions to the Existence and Squeezing of Lagrangian Cobordisms
No full textLisa and I used novel \u27generating family techniques\u27 to study the geometry of Lagrangian submanifolds, answering a basic question in the field. --author-supplied descriptio
Invariants of Legendrian knots in circle bundles
No full textLegendrian knot, contact homology, Morse-Bot
Rational Seifert Surfaces in Seifert Filtered Spaces
No full textRationally null-homologous links in Seifert fibered spaces may be represented combinatorially via labeled diagrams. We introduce an additional condition on a labeled link diagram and prove that it is equivalent to the existence of a rational Seifert surface for the link. In the case when this condition is satisfied, we generalize Seifert\u27s algorithm to explicitly construct a rational Seifert surface for any rationally null-homologous link. As an application of the techniques developed in the paper, we derive closed formulae for the rational Thurston-Bennequin and rotation numbers of a rationally null-homologous Legendrian knot in a contact Seifert fibered space. --author-supplied descriptio
The Correspondence Between Augmentations and Rulings for Legendrian Knots
No full textThis paper investigates connections between two different invariants for Legendrian knots. Though the geometry behind the two invariants, called rulings and augmentations, differs greatly, they are tantalizingly similar to compute in practice. In fact, as this paper shows, there is a connection between the two: namely that one can find the augmentation invariant (an integer) of a Legendrian knot using its ruling invariant (a polynomial). This result provides a starting point for further investigations into connections between the two larger geometric ideas behind the invariants. --author-supplied descriptio
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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