The maximal tubes under the deformations of a class of 3-dimensional hyperbolic cone-manifolds

Recently, Hodgson and Kerckhoff found a small bound on Dehn surgered 3-manifolds from hyperbolic knots not admitting hyperbolic structures using deformations of hyperbolic cone-manifolds. They asked whether the area normalized meridian length squared of maximal tubular neighborhoods of the singular locus of the cone-manifold is decreasing and that summed with the cone angle squared is increasing as we deform the cone-angles. We confirm this near 0 cone-angles for an infinite family of hyperbolic cone-manifolds obtained by Dehn surgeries along the Whitehead link complements. The basic method is based on explicit holonomy computations using the A-polynomials and finding the maximal tubes. One of the key tool is the Taylor expression of a geometric component of the zero set of the A-polynomial in terms of the cone-angles. We also show a sequence of Taylor expressions for Dehn surgered manifolds converges to one for the limit hyperbolic manifold.Comment: 27 pages, 10 figure

Analysis of two-player quantum games in an EPR setting using geometric algebra

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.Comment: 20 pages, no figure, revise

ON TWO-GENERATOR SATELLITE KNOTS

Abstract. Techniques are introduced which determine the geometric structure of non-simple two-generator 3-manifolds from purely algebraic data. As an application, the satellite knots in the 3-sphere with a two-generator presentation in which at least one generator is represented by a meridian for the knot are classified. 1

The free product of groups with amalgamated subgroup malnormal in a single factor

AbstractWe discuss groups that are free products with amalgamation where the amalgamating subgroup is of rank at least two and malnormal in at least one of the factor groups. In 1971, Karrass and Solitar showed that when the amalgamating subgroup is malnormal in both factors, the global group cannot be two-generator. When the amalgamating subgroup is malnormal in a single factor, the global group may indeed be two-generator. If so, we show that either the non-malnormal factor contains a torsion element or, if not, then there is a generating pair of one of four specific types. For each type, we establish a set of relations which must hold in the factor B and give restrictions on the rank and generators of each factor

The Effect of Si Doping on the Electrical Properties of B12As2 Thin Films on (0001) 6H-SiC Substrates

The ability to control the resistivity of the wide band gap semiconductor B12As2 by doping with silicon was verified. The electrical properties of nominally undoped and Si-doped rhombohedral B12As2 thin films on semi-insulating 6H-SiC (0001) substrates prepared by chemical vapor deposition were subjected to Hall effect measurements. Varying the Si concentration in the B12As2 thin films from 7×1018 to 7×1021 at./cm3 (as measured by secondary ion mass spectrometry) decreased the resistivities of the p-type B12As2 films from 2×105 to 10 Ω cm. The resistivities of the B12As2 films were decreased by one to two orders of magnitude after rapid thermal annealing for 30 s in argon. The spatial distribution of the hydrogen concentration was measured before and after annealing. No changes were detected, casting doubt on hydrogen as being the cause for the change in the resistivities of the B12As2 films with annealing