منابع مشابه
Legendrian and Transversal Knots
Contact structures on manifolds and Legendrian and transversal knots in them are very natural objects, born over two centuries ago, in the work of Huygens, Hamilton and Jacobi on geometric optics and work of Lie on partial differential equations. They touch on diverse areas of mathematics and physics, and have deep connections with topology and dynamics in low dimensions. The study of Legendria...
متن کاملTopologically Trivial Legendrian Knots
This paper deals with topologically trivial Legendrian knots in tight and overtwisted contact 3-manifolds. The first parts (Sections 1-3) contain a thorough exposition of the proof of the classification of topologically trivial Legendrian knots (i.e. Legendrian knots bounding embedded 2-disks) in tight contact 3-manifolds (Theorem 1.7), and, in particular, in the standard contact S. These parts...
متن کاملLegendrian Conormals of 2-Knots
LetK be a 2-knot. The conormal Lift ΛK ofK is a Legendrian submanifold in the unit cotangent bundle U∗R4. One can use Legendrian homology on ΛK to define an invariant of K which is a differential graded algebra partly generated by the Reeb chords of ΛK . We try to count and specify these Reeb chords by describing the conormal lifts, of 2-knots given as closed 2dimensional braids, as 1-jet graph...
متن کاملNew Invariants of Legendrian Knots
We discuss two different ways to construct new invariants of Legendrian knots in the standard contact R. These invariants are defined combinatorially, in terms of certain planar projections, and (sometimes) allow to distinguish Legendrian knots which are not Legendrian isotopic but have the same classical invariants.
متن کاملAn Atlas of Legendrian Knots
We present an atlas of Legendrian knots in standard contact three-space. This gives a conjectural Legendrian classification for all knots with arc index at most 9, including alternating knots through 7 crossings and nonalternating knots through 9 crossings. Our method involves a computer search of grid diagrams and applies to transverse knots as well. The atlas incorporates a number of new, sma...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2010
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2010.10.63