Linear slices of the quasifuchsian space of punctured tori

After fixing a marking (V, W) of a quasifuchsian punctured torus group G, the complex length l_V and the complex twist tau_V,W parameters define a holomorphic embedding of the quasifuchsian space QF of punctured tori into C^2. It is called the complex Fenchel-Nielsen coordinates of QF. For a complex number c, let Q_gamma,c be the affine subspace of C^2 defined by the linear equation l_V=c. Then we can consider the linear slice L of QF by QF \cap Q_gamma,c which is a holomorphic slice of QF. For any positive real value c, L always contains the so called Bers-Maskit slice BM_gamma,c. In this paper we show that if c is sufficiently small, then L coincides with BM_gamma,c whereas L has other components besides BM_gamma,c when c is sufficiently large. We also observe the scaling property of L.Comment: 15 pages, 8 figures. arXiv admin note: some text overlap with arXiv:math/020918

PROJECTIVE EMBEDDINGS OF THE TEICHMÜLLER SPACES OF BORDERED RIEMANN SURFACES

We will show that except few cases, by using the hyperbolic length functions of simple closed geodesics, we can embed the Teichmüller space of a bordered Riemann surface into the real projective space of the same dimension. The key idea is to study the hyperbolic structure on a subsurface conformally isomorphic to a torus with a hole (named as a "cook-hat"), or a thrice-punctured sphere with a hole (named as a "crown")

On the Shape of Bers-maskit Slices

We consider complex one-dimensional Bers–Maskit slices through the deformation space of quasifuchsian groups which uniformize a pair of punctured tori. In these slices, the pleating locus on one of the components of the convex hull boundary of the quotient three-manifold has constant rational pleating and constant hyperbolic length. We show that the boundary of such a slice is a Jordan curve which is cusped at a countable dense set of points. We will also show that the slices are not vertically convex, proving the phenomenon observed numerically by Epstein, Marden and Markovic

Spin-polarized saddle points in the topological surface states of the elemental Bismuth revealed by a pump-probe spin-resolved ARPES

We use a pump-probe, spin-, and angle-resolved photoemission spectroscopy (ARPES) with a 10.7 eV laser accessible up to the Brillouin zone edge, and reveal for the first time the entire band structure, including the unoccupied side, for the elemental bismuth (Bi) with the spin-polarized surface states. Our data identify Bi as in a strong topological insulator phase ($Z_2$=1) against the prediction of most band calculations. We unveil that the unoccupied topological surface states possess spin-polarized saddle points yielding the van Hove singularity, providing an excellent platform for the future development of opto-spintronics.Comment: 6 pages, 4 figure