Topology of the Universe and Global Structure

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Akio Hosoya :(1) We have studied the classification of compact and homogeneous universe models based on Thurston's theorem and developed the Hamiltonian description of thecuravature and Teichmuller parameters.(2) We applied the renormalization group equation to the Einstein equation with dust matter and studied the renormalization group flow near the fixed point.(3) We calculated the effect of diffraction and interference of gravitational wave by a rotating massive star and found that the image shifts by a distance proportional to the specific angular momentum of the rotating lens.(4) We have developed a theory in which we probe timelike singularities by finite energy wave packet and showed that most of the known naked singularities are actually harmless. Namely, the wave propagation is perfectly well-defined in that spacetime.Hideki Ishihara :(1) The dynamics of domain wall and graviational wave has been studied and it is found that the degrees of freedom of gravitational wave is completely absorbed bt the domain wall in the case of the Nambu-Goto type.(2) We have studied the propagation of light in an inhomogeneous universe model and studies the effect of inhomogeneities to the distance and red-shift.