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This paper provides a topological interpretation for number theoretic properties of quantum invariants of 3-manifolds. In particular, it is shown that the p-adic valuation of the quantum SO(3)-invariant of a 3-manifold M , for odd primes p, is bounded below by a linear function of the mod p first betti number of M . Sharper bounds using more delicate(More)
Examples are given of prime Legendrian knots in the standard contact 3–space that have arbitrarily many distinct Chekanov polynomials, refuting a conjecture of Lenny Ng. These are constructed using a new “Legendrian tangle replacement” technique. This technique is then used to show that the phenomenon of multiple Chekanov polynomials is in fact quite(More)
To each three-component link in Euclidean 3–space, we associate a generalized Gauss map from the 3–torus to the 2–sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its generalized Gauss map up to homotopy. This generalized Gauss(More)
Three-component links in the 3-dimensional sphere were classified up to link homotopy by John Milnor in his senior thesis, published in 1954. A complete set of invariants is given by the pairwise linking numbers p, q and r of the components, and by the residue class of one further integer μ, the “triple linking number” of the title, which is well-defined(More)
A framing of an oriented trivial bundle is a homotopy class of sections of the associated oriented frame bundle. This paper is a study of the framings of the tangent bundle τM of a smooth closed oriented 3-manifold M , often referred to simply as framings of M .1 We shall also discuss stable framings and 2-framings of M , that is framings of ε1 ⊕ τM (where(More)