منابع مشابه
Quantum Invariants
In earlier work, we derived an expression for a partition function Z, and gave a set of analytic hypotheses under which Z does not depend on a parameter λ. The proof that Z is invariant involved entire cyclic cohomology and K-theory. Here we give a direct proof that d dλ Z = 0. The considerations apply to non-commutative geometry, to super-symmetric quantum theory, to string theory, and to gene...
متن کاملQuantum Invariants * I Introduction
Consider the partition function ZQ(a, g) = 1 √ π ∞ −∞TrH(γU(g)ae −Q2+itda)e−t 2 dt. In this paper we give an elementary proof that this is an invariant. This is what we mean: assume that Q is a self-adjoint operator acting on a Hilbert space H, and that the operator Q is odd with respect to a Z2-grading γ of H. Assume that a is an operator that is even with respect to γ and whose square equals ...
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This is a survey talk on one of the best known quantum knot invariants, the colored Jones polynomial of a knot, and its relation to the algebraic/geometric topology and hyperbolic geometry of the knot complement. We review several aspects of the colored Jones polynomial, emphasizing modularity, stability and effective computations. The talk was given in the Mathematische Arbeitstagung June 24-J...
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The Reshetikhin-Turaev invariant, Turaev’s TQFT, and many related constructions rely on the encoding of certain tangles (n-string links, or ribbon n-handles) as n-forms on the coend of a ribbon category. We introduce the monoidal category of Hopf diagrams, and describe a universal encoding of ribbon string links as Hopf diagrams. This universal encoding is an injective monoidal functor and admi...
متن کاملQuantum Groups and Knot Invariants
Definition 1.1. Informally, a knot is obtained by gluing together the endpoints of a shoelace in R3, considered up to isotopy (but remembering orientation). A link is the same as a knot, but multiple shoelaces are allowed. A tangle consists of (oriented) shoelaces and two parallel sticks, an upper and a lower, which we may glue some endpoints to. In addition, we assign + and − signs to the poin...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2000
ISSN: 0010-3616
DOI: 10.1007/pl00005524