Invariants of 3-manifolds from Representations of the Framed-tangle Category
نویسنده
چکیده
We will construct a monoidal functor (”a monoidal representation”) from the category of framed tangles into the tensor category over a fixed ground vector space which is invariant under Kirby moves and so gives rise to an invariant of 3-manifolds.
منابع مشابه
Reshetikhin–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 کاملar X iv : m at h / 06 11 50 4 v 1 [ m at h . G T ] 1 6 N ov 2 00 6 QUANTUM HYPERBOLIC GEOMETRY
We construct a new family, indexed by the odd integers N ≥ 1, of (2 + 1)-dimensional quantum field theories called quantum hyperbolic field theories (QHFT), and we study its main structural properties. The QHFT are defined for (marked) (2 + 1)-bordisms supported by compact oriented 3-manifolds Y with a properly embedded framed tangle LF and an arbitrary PSL(2,C)character ρ of Y \LF (covering, f...
متن کاملKirby Elements and Quantum Invariants
We define the notion of a Kirby element of a ribbon category C (not necessarily semisimple). Kirby elements lead to 3-manifolds invariants. We characterize a set of Kirby elements (in terms of the structural morphisms of a Hopf algebra in C) which is sufficiently large to recover the quantum invariants of 3-manifolds of Reshetikhin-Turaev, of Hennings-Kauffman-Radford, and of Lyubashenko. The c...
متن کاملOn 3-manifold Invariants Arising from Finite-dimensional Hopf Algebras
We reformulate Kauffman’s method of defining invariants of 3-manifolds intrinsically in terms of right integrals on certain finite dimensional Hopf algebras and define a type of universal invariants of framed tangles and invariants of 3-manifolds.
متن کاملBottom 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 کامل