On continuous extension of grafting maps

The definition of the grafting operation for quasifuchsian groups is extended by Bromberg to all $b$-groups. Although the grafting maps are not necessarily continuous at boundary groups, in this paper, we show that the grafting maps take every "standard" convergent sequence to a convergent sequence. As a consequence of this result, we extend Goldman's grafting theorem for quasifuchsian groups to all boundary $b$-groups.Comment: 24 pages, 2 figure

Exotic projective structures and quasifuchsian spaces II

Let $P(S)$ be the space of projective structures on a closed surface $S$ of genus $g >1$ and let $Q(S)$ be the subset of $P(S)$ of projective structures with quasifuchsian holonomy. It is known that $Q(S)$ consists of infinitely many connected components. In this paper, we will show that the closure of any exotic component of $Q(S)$ is not a topological manifold with boundary and that any two components of $Q(S)$ have intersecting closures.Comment: 22 pages, 9 figure

An extension of the Maskit slice for 4-dimensional Kleinian groups

Let $\Gamma$ be a 3-dimensional Kleinian punctured torus group with ccidental parabolic transformations. The deformation space of $\Gamma$ in the group of M\"{o}bius transformations on the 2-sphere is well-known as the Maskit slice of punctured torus groups. In this paper, we study deformations $\Gamma'$ of $\Gamma$ in the group of M\"{o}bius transformations on the 3-sphere such that $\Gamma'$ does not contain screw parabolic transformations. We will show that the space of the deformations is realized as a domain of 3-space $\mathbb{R}^3$, which contains the Maskit slice of punctured torus groups as a slice through a plane. Furthermore, we will show that the space also contains the Maskit slice of fourth-punctured sphere groups as a slice through another plane. Some of another slices of the space will be also studied.Comment: 34 pages, 11 figures. v3: The title is changed and some typo are fixed. To appear in Conform. Geom. dyn. The paper including more clear figures can be downloaded from http://www.math.nagoya-u.ac.jp/~itoken/index.htm

Probing GHz Gravitational Waves with Graviton-magnon Resonance

A novel method for extending frequency frontier in gravitational wave observations is proposed. It is shown that gravitational waves can excite a magnon. Thus, gravitational waves can be probed by a graviton-magnon detector which measures resonance fluorescence of magnons. Searching for gravitational waves with a wave length $\lambda$ by using a ferromagnetic sample with a dimension $l$, the sensitivity of the graviton-magnon detector reaches spectral densities, around $5.4 \times 10^{-22} \times (\frac{l}{\lambda /2\pi})^{-2} \ [{\rm Hz}^{-1/2}]$at 14 GHz and$8.6 \times 10^{-21} \times (\frac{l}{\lambda /2\pi})^{-2} \ [{\rm Hz}^{-1/2}]$ at 8.2 GHz, respectively.Comment: 5 pages, 1 figure, minor change