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...

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 ...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...