OGUNI, Shinichi

Graduate School of Science and Engineering Mathematics Physics and Earth Sciences
PositionAssociate Professor
Last Updated :2019/02/07

Research Activities

Published Papers


  • Coarse compactifications and controlled products
    Tomohiro Fukaya, Shin-ichi Oguni, Takamitsu Yamauchi,   2018 10 20 , 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,   2012 01 , 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,   2011 09 , 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,   2010 08 , 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.

Conference Activities & Talks

  • On a coarse Cartan-Hadamard theorem
    Shin-ichi Oguni, Rigidity School ― The Final Meeting,   2018 09
  • On coarse homotopy
    Shin-ichi Oguni, Research Trends on Set-theoretic and Geometric Topology and their cooperation with various branches,   2017 06
  • Coronae of product spaces and the coarse Baum-Connes conjecture
    Shin-ichi Oguni, Conference on Non-commutative Geometry and K-Theory,   2015 12
  • Coarse Baum-Connes conjecture and coarse algebraic topology
    Shin-ichi Oguni, Rigidity School, Tokyo 2013/2014,   2014 01
  • Coronae and coarse homologies
    Shin-ichi Oguni, Metric geometry and analysis,   2013 12
  • On the coarse Baum-Connes conjecture
    Shin-ichi Oguni, GEOQUANT 2013,   2013 08

Research Grants & Projects

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