1,135 research outputs found
On continuous extension of grafting maps
The definition of the grafting operation for quasifuchsian groups is extended
by Bromberg to all -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 -groups.Comment: 24 pages, 2 figure
Exotic projective structures and quasifuchsian spaces II
Let be the space of projective structures on a closed surface of
genus and let be the subset of of projective structures
with quasifuchsian holonomy. It is known that consists of infinitely
many connected components. In this paper, we will show that the closure of any
exotic component of is not a topological manifold with boundary and that
any two components of have intersecting closures.Comment: 22 pages, 9 figure
An extension of the Maskit slice for 4-dimensional Kleinian groups
Let be a 3-dimensional Kleinian punctured torus group with ccidental
parabolic transformations. The deformation space of 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 of
in the group of M\"{o}bius transformations on the 3-sphere such that
does not contain screw parabolic transformations. We will show that
the space of the deformations is realized as a domain of 3-space
, 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 by using a ferromagnetic sample with a
dimension , the sensitivity of the graviton-magnon detector reaches spectral
densities, around $5.4 \times 10^{-22} \times (\frac{l}{\lambda /2\pi})^{-2} \
[{\rm Hz}^{-1/2}]8.6 \times 10^{-21} \times (\frac{l}{\lambda
/2\pi})^{-2} \ [{\rm Hz}^{-1/2}]$ at 8.2 GHz, respectively.Comment: 5 pages, 1 figure, minor change
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