Determinations of rational Dedekind - zeta invariants of hyperbolic manifolds and Feynman knots and links
نویسنده
چکیده
We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers a and b giving
منابع مشابه
Eta Invariants and Regularized Determinants for Odd Dimensional Hyperbolic Manifolds with Cusps
We study eta invariants of Dirac operators and regularized determinants of Dirac Laplacians over hyperbolic manifolds with cusps. We follow Werner Müller (see [18], [19]) and use relative traces to define the eta function and the zeta function. We show regularities of eta and zeta functions at the origin so that we can define the eta invariant and the regularized determinant. By the Selberg tra...
متن کاملStable Concordance of Knots in 3–manifolds
Knots and links in 3-manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato-Levine invariants, and Milnor’s triple linking numbers. Besides fitting into a general theory of Whitney towers, these invariants provide obstructions to the existence of a singular concordance which can be homotoped ...
متن کاملDehn Surgery on Arborescent Links 3
This paper studies Dehn surgery on a large class of links, called arborescent links. It will be shown that if an arborescent link L is suuciently complicated, in the sense that it is composed of at least 4 rational tangles T (p i =q i) with all q i > 2, and none of its length 2 tangles are of the form T (1=2q 1 ; 1=2q 2), then all complete surgeries on L produce Haken manifolds. The proof needs...
متن کاملQuantum Topology and Quantum Computing
I. Introduction This paper is a quick introduction to key relationships between the theories of knots,links, three-manifold invariants and the structure of quantum mechanics. In section 2 we review the basic ideas and principles of quantum mechanics. Section 3 shows how the idea of a quantum amplitude is applied to the construction of invariants of knots and links. Section 4 explains how the ge...
متن کاملInvariants for 1-dimensional Cohomology Classes Arising from Tqft
Let (V,Z) be a Topological Quantum Field Theory over a field f defined on a cobordism category whose morphisms are oriented n+1-manifolds perhaps with extra structure (for example a p1 structure and banded link). Let (M,χ) be a closed oriented n+ 1-manifold M with this extra structure together with χ ∈ H1(M). Let M∞ denote the infinite cyclic cover of M given by χ. Consider a fundamental domain...
متن کامل