OGUNI Shin-ichi

J-GLOBAL         Last updated: Aug 30, 2019 at 09:51
 
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Name
OGUNI Shin-ichi
Affiliation
Ehime University

Published Papers

 
Ryosuke Mineyama, Shin-ichi Oguni
Monatshefte fur Mathematik   187(4) 665-680   Dec 2018   [Refereed]
© 2018, Springer-Verlag GmbH Austria, part of Springer Nature. We begin a coarse geometric study of Hilbert geometry. Actually we give a necessary and sufficient condition for the natural boundary of a Hilbert geometry to be a corona, which is a n...
Tomohiro Fukaya, Shin-ichi Oguni
Journal of Topology and Analysis   to appear    [Refereed]
We establish a coarse version of the Cartan-Hadamard theorem, which states
that proper coarsely convex spaces are coarsely homotopy equivalent to the open
cones of their ideal boundaries. As an application, we show that such spaces
satisfy the coa...
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
Tokyo Journal of Mathematics   42 83-112   Jun 2019   [Refereed]
We consider two families of subgroups of a group. Each subgroup which belongs
to one family is contained in some subgroup which belongs to the other family.
We then discuss relations of relative hyperbolicity for the group with respect
to the two ...
Tomohiro Fukaya, Shin-ichi Oguni
Journal of Topology and Analysis   8 431-474   Sep 2016   [Refereed]
© 2016 World Scientific Publishing Company.We construct a corona of a relatively hyperbolic group by blowing-up all parabolic points of its Bowditch boundary. We relate the K-homology of the corona with the K-theory of the Roe algebra, via the coa...
Shin-ichi Oguni
Sūgaku   68(2) 177-199   Apr 2016   [Refereed]
Tomohiro Fukaya, Shin-ichi Oguni
Kyoto Journal of Mathematics   56 1-12   Apr 2016   [Refereed]
© 2016 by Kyoto University.We prove that the coarse assembly maps for proper metric spaces that are nonpositively curved in the sense of Busemann are isomorphisms, where we do not assume that the spaces have bounded coarse geometry. Also it is sho...
Tomohiro Fukaya, Shin-ichi Oguni
Advances in Mathematics   279 201-233   Jul 2015   [Refereed]
© 2015 Elsevier Inc. We study the coarse Baum-Connes conjecture for product spaces and product groups. We show that a product of CAT(0) groups, polycyclic groups and relatively hyperbolic groups which satisfy some assumptions on peripheral subgrou...
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata, K. Matsuzaki
Tokyo Journal of Mathematics   38 99-123   Jan 2015   [Refereed]
We define relatively quasiconvex subgroups of relatively hyperbolic groups in the sense of Osin and show that such subgroups have expected properties. Also we state several definitions equivalent to the definition of relatively hyperbolic groups i...
Matsuda Yoshifumi, Oguni Shin-ichi, Yamagata Saeko
RIMS Kokyuroku Bessatsu   48 73-93   Jun 2014   [Refereed]
Yoshifumi Matsuda, Shin-ichi Oguni
Journal of Group Theory   17 41-47   Jan 2014   [Refereed]
Baker and Riley gave an inclusion of a free group of rank 3 in a hyperbolic group for which the Cannon Thurston map is not well-defined. By using their result, we show that every non-elementary hyperbolic group can be included in some hyperbolic g...
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
Houston Journal of Mathematics   39 1291-1299   Dec 2013   [Refereed]
We prove that a countable group with an e ective minimal non-elementary convergence group action is a Powers group. More strongly we prove that it is a strongly Powers group and thus its non-trivial subnormal subgroups are C*-simple. © 2013 Univer...
Shin-ichi Oguni
Noncommutative Geometry and Physics, 3   433-469   Mar 2013   [Refereed]
We have two purposes in this paper. One is to define and to study dilatational equivalence classes and Novikov-Shubin type capacities of arbitrary discrete groups from an algebraic viewpoint. The other is to refine some known results about asympto...
Tomohiro Fukaya, Shin-ichi Oguni
Journal of Topology and Analysis   4 99-113   Mar 2012   [Refereed]
We study a group which is hyperbolic relative to a finite family of infinite subgroups. We show that the group satisfies the coarse BaumConnes conjecture if each subgroup belonging to the family satisfies the coarse Baum-Connes conjecture and admi...
Shin-ichi Oguni
Kyoto Journal of Mathematics   47 359-369   Jan 2007   [Refereed]
We introduce an algorithm which transforms a finitely presented group G into another one GΨ. By using this, we can get many finitely presented groups whose group homology with coefficients in the group von Neumann algebra vanish, that is, many cou...
Shin-ichi Oguni
Journal of the Mathematical Society of Japan   59 223-237   Jan 2007   [Refereed]
We define new L2-invariants which we call secondary Novikov-Shubin invariants. We calculate the first secondary Novikov-Shubin invariants of finitely generated groups by using random walk on Cayley graphs and see in particular that these are invar...

Misc

 
Tomohiro Fukaya, Shin-ichi Oguni, Takamitsu Yamauchi
   Oct 2018
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 t...
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
   Jan 2012
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...
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
   Sep 2011
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.
Shin-ichi Oguni
preprint      Aug 2010
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-i...

Conference Activities & Talks

 
Shin-ichi Oguni
AMS Sectional meeting   Mar 2019   
Shin-ichi Oguni
Rigidity School ― The Final Meeting   Sep 2018   
Shin-ichi Oguni
Research Trends on Set-theoretic and Geometric Topology and their cooperation with various branches   Jun 2017   
Coronae of product spaces and the coarse Baum-Connes conjecture
Shin-ichi Oguni
Conference on Non-commutative Geometry and K-Theory   Dec 2015   
Shin-ichi Oguni
Rigidity School, Tokyo 2013/2014   Jan 2014   
Shin-ichi Oguni
Metric geometry and analysis   Dec 2013   
On the coarse Baum-Connes conjecture
Shin-ichi Oguni
GEOQUANT 2013   Aug 2013   

Association Memberships

 
 

Research Grants & Projects

 
粗Baum-Connes予想に関わる粗幾何学
JSPS: Grant-in-Aid for Young Scientists (B)
Project Year: Apr 2016 - Mar 2020    Investigator(s): OGUNI Shin-ichi
離散群の相対的双曲構造と収束群作用
JSPS: Grant-in-Aid for Young Scientists (B)
Project Year: Apr 2012 - Mar 2016    Investigator(s): OGUNI Shin-ichi
離散群の相対双曲構造
愛媛大学: 理学部長裁量研究助成費
Project Year: Apr 2011 - Mar 2012    Investigator(s): OGUNI Shin-ichi
普遍的な幾何学的有限収束作用を持つ離散群 の探求とそのような離散群の性質の研究
愛媛大学: 理学部長裁量研究助成費
Project Year: Apr 2010 - Mar 2011    Investigator(s): OGUNI Shin-ichi

Social Contribution

 
[Planner]  (Kyoto University)  8 Sep 2015 - 11 Sep 2015
[Planner]  (Kyoto university)  9 Dec 2013 - 13 Dec 2013
[Planner]  (Kyoto University)  12 Mar 2012 - 15 Mar 2012