Researcher Database

OGUNI, Shinichi

FacultyGraduate School of Science and Engineering Mathematics Physics and Earth Sciences
PositionAssociate Professor
Last Updated :2019/04/16

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  • Name

    OGUNI, Shinichi

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  • Coarse compactifications and controlled products, Tomohiro Fukaya, Shin-ichi Oguni, Takamitsu Yamauchi, 20181020,, We introduce the notion of controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gromov boundaries. It is shown that the Gromov boundary with respect to a controlled product on a proper metric space complements the space as a coarse compactification. It is also shown that there is a bijective correspondence between the set of all coarse equivalence classes of controlled products and the set of all equivalence classes of coarse compactifications.
  • Blowing up and down compacta with geometrically finite convergence actions of a group, Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata, 20120100,, We consider two compacta with minimal non-elementary convergence actions of a countable group. When there exists an equivariant continuous map from one to the other, we call the first a blow-up of the second and the second a blow-down of the first. When both actions are geometrically finite, it is shown that one is a blow-up of the other if and only if each parabolic subgroup with respect to the first is parabolic with respect to the second. As an application, for each compactum with a geometrically finite convergence action, we construct its blow-downs with convergence actions which are not geometrically finite.
  • Hyperbolically embedded virtually free subgroups of relatively hyperbolic groups, Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata, 20110900,, We show that if a group is not virtually cyclic and is hyperbolic relative to a family of proper subgroups, then it has a hyperbolically embedded subgroup which contains a finitely generated non-abelian free group as a finite index subgroup.
  • L2-invariants of groups under coarse equivalence and of groupoids under Morita equivalence, Shin-ichi Oguni, preprint, 20100800, We prove that triviality of some L2-invariants of discrete groups is preserved by coarse equivalence, where L2-invariants are L2-homologies, L2-Betti numbers (with `a mild condition') and Novikov-Shubin invariants. We give definitions of some L2-invariants of cocompact etale groupoids and prove that their triviality is preserved by Morita equivalence. Also we exhibit basic properties for modules over von Neumann algebras which are not necessarily finite. This paper contains an appendix by Yamashita, where a characterization of finite von Neumann algebras is given.

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