منابع مشابه
Transversely Non Simple Knots
By proving a connected sum formula for the Legendrian invariant λ+ in knot Floer homology we exhibit infinitely many transversely non simple knots. Moreover we construct knots admitting many non-isotopic transverse representatives with equal selflinking number.
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A knot k in a closed orientable 3-manifold is called nonsimple if the exterior of k possesses a properly embedded essential surface of nonnegative Euler characteristic. We show that if k is a nonsimple prime tunnel number one knot in a lens space M (where M does not contain any embedded Klein bottles), then k is a (1, 1) knot. Elements of the proof include handle addition and Dehn filling resul...
متن کاملA-polynomials of a Family of Two-bridge Knots
The J(k, l) knots, often called the double twist knots, are a subclass of two-bridge knots which contains the twist knots. We show that the A-polynomial of these knots can be determined by an explicit resultant. We present this resultant in two different ways. We determine a recursive definition for the A-polynomials of the J(4, 2n) and J(5, 2n) knots, and for the canonical component of the A-p...
متن کاملObstructing Sliceness in a Family of Montesinos Knots
Using Gauge theoretical techniques employed by Lisca for 2-bridge knots and by Greene-Jabuka for 3-stranded pretzel knots, we show that no member of the family of Montesinos knots M(0; [m1 + 1, n1 + 2], [m2 + 1, n2 + 2], q), with certain restrictions on mi, ni, and q, can be (smoothly) slice. Our techniques use Donaldson’s diagonalization theorem and the fact that the 2-fold covers of Montisino...
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...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2010
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2010.10.293