Bottom tangles and universal invariants
نویسندگان
چکیده
منابع مشابه
Bottom tangles and universal invariants
A bottom tangle is a tangle in a cube consisting only of arc components, each of which has the two endpoints on the bottom line of the cube, placed next to each other. We introduce a subcategory B of the category of framed, oriented tangles, which acts on the set of bottom tangles. We give a finite set of generators of B , which provides an especially convenient way to generate all the bottom t...
متن کاملOn the universal sl2 invariant of ribbon bottom tangles
A bottom tangle is a tangle in a cube consisting of arc components whose boundary points are on a line in the bottom square of the cube. A ribbon bottom tangle is a bottom tangle whose closure is a ribbon link. For every n-component ribbon bottom tangle T , we prove that the universal invariant JT of T associated to the quantized enveloping algebra Uh(sl2) of the Lie algebra sl2 is contained in...
متن کاملOn the universal sl2 invariant of boundary bottom tangles
The universal sl2 invariant of bottom tangles has a universality property for the colored Jones polynomial of links. Habiro conjectured that the universal sl2 invariant of boundary bottom tangles takes values in certain subalgebras of the completed tensor powers of the quantized enveloping algebra Uh(sl2) of the Lie algebra sl2. In the present paper, we prove an improved version of Habiro’s con...
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The notion of a chord diagram emerged from Vassiliev's work Vas90], Vas92] (see also Gusarov Gus91], Gus94] and Bar-Natan BN91], BN95]). Slightly later, Kontsevich Kon93] deened an invariant of classical knots taking values in the algebra generated by formal linear combinations of chord diagrams modulo the four-term relation. This knot invariant establishes an isomorphism of a projective limit ...
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Given a compact, connected, oriented 3-manifold M with boundary, and epimorphism χ from H1M to a free abelian group Π, two invariants β, τ ∈ ZΠ are defined. If M embeds in another such 3manifold N such that χN factors through χ, then the product βτ divides ∆0(H1Ñ). A theorem of D. Krebes concerning 4-tangles embedded in links arises as a special case. Algebraic and skein theoretic generalizatio...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2006
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2006.6.1113