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This paper describes a family of pseudo–Anosov braids with small dilatation. The smallest dilatations occurring for braids with 3, 4 and 5 strands appear in this family. A pseudo-Anosov braid with 2g + 1 strands determines a hyperelliptic mapping class with the same dilatation on a genus–g surface. Penner showed that logarithms of least dilatations of(More)
We consider a hyperbolic surface bundle over the circle with the smallest known volume among hyperbolic manifolds having 3 cusps, so called “the magic manifold” M = Mmagic. We compute the entropy function on the fiber face ∆ ⊂ H2(M,∂M ;R), determine homology classes whose representatives are genus 0 fiber surfaces, and describe their monodromies by braids.(More)
We discuss a comparison of the entropy of pseudo-Anosov maps and the volume of their mapping tori. Recent study of Weil-Petersson geometry of the Teichmüller space tells us that they admit linear inequalities for both directions under some bounded geometry condition. Based on the experiments, we present various observations on the relation between minimal(More)
The dilatation of a pseudo-Anosov braid is a conjugacy invariant. In this paper, we study the dilatation of a special family of pseudo-Anosov braids. We prove an inductive formula to compute their dilatation, a monotonicity and an asymptotic behavior of the dilatation for this family of braids. We also give an example of a family of pseudo-Anosov braids(More)
Let K be a knot or link in S3 which is fibred — the complement fibres over S1 with fibres spanning surfaces. We focus on those fibred knots and links which have the following property: every vector field transverse to the fibres possesses closed flow lines of all possible knot and link types in S3 . Our main result is that a large class of fibred knots and(More)
The effects of various energy poisons on oxidation of respiratory substrate, synthesis of cellular ATP, and energy transformation reaction in intact Escherichia coli cells were studied systematically. Various mutants were, therefore, used in which specific functions in the energy-transducing reactions were defective or altered. The energy poisons examined(More)