Framed holonomic knots
نویسندگان
چکیده
منابع مشابه
Framed holonomic knots
Abstract A holonomic knot is a knot in 3-space which arises as the 2-jet extension of a smooth function on the circle. A holonomic knot associated to a generic function is naturally framed by the blackboard framing of the knot diagram associated to the 1-jet extension of the function. There are two classical invariants of framed knot diagrams: the Whitney index (rotation number) W and the self ...
متن کاملFramed Knots in 3-manifolds
For a fixed isotopy type K of unframed knots in S there are infinitely many isotopy classes of framed knots that correspond to K when we forget the framing. We show that the same fact is true for all the isotopy types of unframed knots in a closed oriented 3-manifold M , provided that M 6= (S × S)#M . On the other hand for any M = (S × S)#M ′ we construct examples of isotopy classes of unframed...
متن کاملFramed Knots at Large N
We study the framing dependence of the Wilson loop observable of U(N) ChernSimons gauge theory at large N . Using proposed geometrical large N dual, this leads to a direct computation of certain topological string amplitudes in a closed form. This yields new formulae for intersection numbers of cohomology classes on moduli of Riemann surfaces with punctures (including all the amplitudes of pure...
متن کاملEuclidean Geometric Invariant of Framed Knots in Manifolds
We present an invariant of a three–dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.
متن کاملFramed Knots in 3-manifolds and Affine Self-linking Numbers
The number |K| of non-isotopic framed knots that correspond to a given unframed knot K ⊂ S is infinite. This follows from the existence of the self-linking number slk of a zerohomologous framed knot. We use the approach of Vassiliev-Goussarov invariants to construct “affine self-linking numbers” that are extensions of slk to the case of nonzerohomologous framed knots. As a corollary we get that...
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: 2002
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2002.2.449