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...

Nagoya Mathematical Journal 202 1-13 Jul 2011 [Refereed]

We study semigroup actions on a coarse space and the induced actions on the Higson corona from a dynamical point of view. Our main theorem states that if an action of an abelian semigroup on a proper coarse space satisfies certain conditions, the ...

Homology, Homotopy and Applications 10 195-209 Nov 2008 [Refereed]

For n = 2m+1 - 4, m ≥ 2, we determine the cup-length of H*(G̃n,3; ℤ/2) by finding a Gröbner basis associated with a certain subring, where G̃n,3 is the oriented Grassmann manifold SO(n + 3)/SO(n) x SO(3). As an application, we provide not only a l...

A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture

Tomohiro FUKAYA

To appear in Journal of Topology and Analysis [Refereed]

arXiv:1705.05588
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 space...