尾國 新一

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研究者氏名
尾國 新一
所属
愛媛大学

論文

 
Tomohiro Fukaya, Shin-ichi Oguni
Journal of Topology and Analysis   to appear    [査読有り]
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   to appear    [査読有り]
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 ...
Ryosuke Mineyama, Shin-ichi Oguni
Monatshefte fur Mathematik   187(4) 665-680   2018年12月   [査読有り]
© 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   8 431-474   2016年9月   [査読有り]
© 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...
Tomohiro Fukaya, Shin-ichi Oguni
Kyoto Journal of Mathematics   56 1-12   2016年4月   [査読有り]
© 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...
尾國 新一
数学   68(2) 177-199   2016年4月   [査読有り]
Tomohiro Fukaya, Shin-ichi Oguni
Advances in Mathematics   279 201-233   2015年7月   [査読有り]
© 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   2015年1月   [査読有り]
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   2014年6月   [査読有り]
Yoshifumi Matsuda, Shin-ichi Oguni
Journal of Group Theory   17 41-47   2014年1月   [査読有り]
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   2013年12月   [査読有り]
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   2013年3月   [査読有り]
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   2012年3月   [査読有り]
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   2007年1月   [査読有り]
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   2007年1月   [査読有り]
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
   2018年10月
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
   2012年1月
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
   2011年9月
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年8月
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...

講演・口頭発表等

 
尾國 新一
トポロジー火曜セミナー(東大数理)   2018年11月6日   
Shin-ichi Oguni
Rigidity School ― The Final Meeting   2018年9月   
尾國 新一
日本数学会2018年度年会   2018年3月   
尾國 新一
ワークショップ:幾何学的群論の新展開   2018年2月   
尾國 新一
松山TGSAセミナー   2017年10月   
Shin-ichi Oguni
集合論的・幾何学的トポロジーの動向と諸分野との連携   2017年6月   
尾國新一
第3回幾何学的群論若手勉強会   2017年3月   
Hilbert幾何の粗幾何的性質
白浜研究集会   2016年3月   
尾國新一
春の代数的位相幾何学セミナー~幾何的アプローチ   2016年3月   
Coronae of product spaces and the coarse Baum-Connes conjecture
Shin-ichi Oguni
Conference on Non-commutative Geometry and K-Theory   2015年12月   
尾國新一
広島幾何学研究集会2015   2015年10月   
尾國 新一
松山TGSAセミナー   2015年6月   
尾國新一
日本数学会2014年度秋季総合分科会   2014年9月   
Shin-ichi Oguni
Rigidity School, Tokyo 2013/2014   2014年1月   
Shin-ichi Oguni
Metric geometry and analysis   2013年12月   
An introduction to the coarse Baum-Connes conjecture
尾國新一
非可換幾何 湯谷研究集会   2013年11月   
On the coarse Baum-Connes conjecture
Shin-ichi Oguni
GEOQUANT 2013   2013年8月   

所属学協会

 
 

競争的資金等の研究課題

 
粗Baum-Connes予想に関わる粗幾何学
日本学術振興会: 科学研究費若手B
研究期間: 2016年4月 - 2020年3月    代表者: 尾國 新一
離散群の相対的双曲構造と収束群作用
日本学術振興会: 科学研究費若手B
研究期間: 2012年4月 - 2016年3月    代表者: 尾國 新一
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
研究期間: 2011年4月 - 2012年3月    代表者: 尾國 新一
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
研究期間: 2010年4月 - 2011年3月    代表者: 尾國 新一

社会貢献活動

 
【企画】  (ルネッサ赤沢(静岡県伊東市))  2018年2月5日 - 2018年2月8日
【企画】  (ルネッサ赤沢(静岡県伊東市))  2017年3月7日 - 2017年3月10日
【その他】  (愛媛大学理学部)  2017年1月22日 - 2017年1月22日
Osajda's Monster 勉強会
【企画】  (ルネッサ赤沢(静岡県伊東市))  2016年1月4日 - 2016年1月7日
【企画】  (京都大学理学部)  2015年9月8日 - 2015年9月11日