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In this paper we give a complete description of the space QF of quasifuchsian punctured torus groups in terms of what we call pleating invariants. These are natural invariants of the boundary ∂C of the convex core of the associated hyperbolic 3-manifold M and give coordinates for the non-Fuchsian groups QF − F. The pleating invariants of a component of ∂C(More)
The pathologies of many infectious, autoimmune and malignant diseases are influenced by the profiles of cytokine production in pro-inflammatory (TH1) and anti-inflammatory (TH2) T cells. Interindividual differences in cytokine profiles appear to be due, at least in part, to allelic polymorphism within regulatory regions of cytokine gene. Many studies have(More)
Within the past few years, the focus on cytokine single nucleotide polymorphism (SNP) function and association with human diseases has increased considerably. This third supplement to the Cytokine Gene Polymorphism in Human Disease: On-line database describes the positive associations of cytokine SNPs in human diseases described in articles published from(More)
Let G ⊂ P SL(2, C) be a geometrically finite Kleinian group, with region of discontinuity Ω(G). By Ahlfors' finiteness theorem, the quotient, Ω(G)/G, is a finite union of Riemann surfaces of finite type. Thus on it, there are only finitely many mutually disjoint free homotopy classes of simple closed curves. It is shown in [9] and [13] that if γ 1 ,. .. , γ(More)
We study the the tangent family F = {λ tan z, λ ∈ C − {0}} and give a complete classification of their stable behavior. We also characterize the the hyperbolic components and give a combinatorial description of their deployment in the parameter plane.
In addition to being packed with fundamental material important for every beginner in complex analysis, in expeditious and intuitive terms this little book transports the reader through a range of interesting topics in one-dimensional hyperbolic geometry, discrete subgroups, holomorphic dynamics and iterated function systems. In chapter after chapter, one(More)
Conjugacy classes of primitive words in the free group of rank two can be indexed by the rationals. A representative for each conjugacy class is given by a recursive enumeration scheme and the representative, usually called a Farey word, is denoted by W p/q where p and q are relatively prime integers. Each such primitive word is known to be conjugate to(More)