An intrinsic approach to invariants of framed links in 3-manifolds
نویسندگان
چکیده
We study framed links in irreducible 3-manifolds that are Z-homology 3spheres or atoroidal Q-homology 3-spheres. We calculate the dual of the Kauffman skein module over the ring of two variable power series with complex coefficients. For links in S we give a new construction of the classical Kauffman polynomial.
منابع مشابه
An Intrinsic Approach to Polynomial Invariants for Links in 3-manifolds
We study framed links in irreducible Z-homology 3-spheres and we provide sufficient conditions under which an invariant defined on singular links with one transverse double point gives rise to an invariant of framed links. Our results also hold for framed links in atoroidal, Q-homology 3-spheres. As an application we obtain a 2-variable formal power series invariant for framed links that satisf...
متن کاملQuantum Deformations of Fundamental Groups of Oriented 3-manifolds
We compute two-term skein modules of framed oriented links in oriented 3-manifolds. They contain the self-writhe and total linking number invariants of framed oriented links in a universal way. The relations in a natural presentation of the skein module are interpreted as monodromies in the space of immersions of circles into the 3-manifold.
متن کاملQuantum Invariants of Periodic Links and Periodic 3-manifolds
We give criteria for framed links and 3-manifolds to be periodic of prime order. As applications we show that the Poincare sphere is of periodicity 2, 3, 5 only and the Brieskorn sphere (2,3,7) is of periodicity 2, 3, 7 only.
متن کاملReshetikhin–Turaev invariants of Seifert 3–manifolds and a rational surgery formula
We calculate the RT–invariants of all oriented Seifert manifolds directly from surgery presentations. We work in the general framework of an arbitrary modular category as in [Tu], and the invariants are expressed in terms of the S– and T –matrices of the modular category. In another direction we derive a rational surgery formula, which states how the RT– invariants behave under rational surgery...
متن کاملCongruence and Similarity of 3-manifolds
Let f be an integer greater than one. Type-f surgery is a kind of surgery along a knot in a 3-manifold which generalizes the notion of n/f surgery in a homology sphere. Such surgeries preserves the cohomology groups with Zf coefficients. Type-f surgery generates an equivalence relation on 3manifolds which we call similarity modulo f . If f is odd, we show that typef surgery also preserves the c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011