Spin networks, Turaev-Viro theory and the loop representation
نویسندگان
چکیده
منابع مشابه
Building Blocks in Turaev-Viro Theory
Abstract We study the form of the Turaev-Viro partition function Z(M) for different 3-manifolds with boundary. We show that for S2 boundaries Z(M) factorizes into a term which contains the boundary dependence and another which depends only on the topology of the underlying manifold. From this follows easily the formula for the connected sum of two manifolds Z(M#N ). For general Tg boundaries th...
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We show that the Hilbert space basis that defines the Ponzano-Regge-Turaev-Viro-Ooguri combinatorial definition of 3-d Quantum Gravity is the same as the one that defines the Loop Representation. We show how to compute lengths in Witten's 3-d gravity and how to reconstruct the 2-d geometry from a state of Witten's theory. We show that the non-degenerate geometries are contained in the Witten's ...
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A Turaev–Viro invariant is a state sum, i.e., a polynomial that can be read off from a special spine or a triangulation of a compact 3-manifold. If the polynomial is evaluated at the solution of a certain system of polynomial equations (Biedenharn–Elliott equations) then the result is a homeomorphism invariant of the manifold (" numerical Turaev-Viro invariant "). The equation system defines an...
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The Turaev-Viro invariants are a powerful family of topological invariants for distinguishing between different 3-manifolds. They are invaluable for mathematical software, but current algorithms to compute them require exponential time. The invariants are parameterised by an integer r ≥ 3. We resolve the question of complexity for r = 3 and r = 4, giving simple proofs that computing Turaev-Viro...
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Given an oriented knot K in S and a TQFT, Turaev and Viro defined modules somewhat analogous to the Alexander module. We work with the (Vp, Zp) theories of Blanchet, Habegger, Masbaum and Vogel [BHMV] for p ≥ 3, and consider the associated modules. In [G], we defined modules which also depend on the extra data of a color c which is assigned to a meridian of the knot in the construction of the m...
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ژورنال
عنوان ژورنال: Classical and Quantum Gravity
سال: 1995
ISSN: 0264-9381,1361-6382
DOI: 10.1088/0264-9381/12/4/006