TY - JOUR
T1 - The coarse Baum-Connes conjecture for relatively hyperbolic groups
AU - Fukaya, Tomohiro
AU - Oguni, Shin Ichi
N1 - Funding Information:
T. F. was supported by Grant-in-Aid for Young Scientists (B) (23740049) from the Ministry of Education, Culture, Sports, Science and Technology.
PY - 2012/3
Y1 - 2012/3
N2 - 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 admits a finite universal space for proper actions. If the group is torsion-free, then it satisfies the analytic Novikov conjecture.
AB - 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 admits a finite universal space for proper actions. If the group is torsion-free, then it satisfies the analytic Novikov conjecture.
KW - Coarse Baum-Connes conjecture
KW - Mayer-Vietoris sequence
KW - relatively hyperbolic group
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U2 - 10.1142/S1793525312500021
DO - 10.1142/S1793525312500021
M3 - Article
AN - SCOPUS:84859918459
VL - 4
SP - 99
EP - 113
JO - Journal of Topology and Analysis
JF - Journal of Topology and Analysis
SN - 1793-5253
IS - 1
ER -