The Novikov conjecture for hyperbolic foliations

被引：81

作者：

Tu, JL ^{[1
]}

机构：

[1] Univ Paris 06, Math Inst, F-75252 Paris 05, France

来源：

K-THEORY | 1999年 / 16卷 / 02期

关键词：

C*-algebra; equivariant KK-theory; groupoid; foliation; Baum-Connes conjecture; Novikov conjecture;

D O I：

10.1023/A:1007756501903

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define the notion of 'bolicity' for foliations, which is a weaker notion than Gromov's hyperbolicity, and we prove the Novikov conjecture for foliations with compact base and whose holonomy groupoid is Hausdorff, by showing that the Baum-Connes map is injective. This result generalizes that of Kasparov and Skandalis in the case of 'bolic' groups.

引用

页码：129 / 184

页数：56

共 25 条

[1]

BAAJ S, 1989, K-THEORY, V2, P683

[2]

BAUM P, 1982, P SYMP PURE MATH, V38, P117

[3]

BAUM P, 1982, GEOMETRIC K THEORY L

[4]

BAUM P, 1983, LEAFWISE HOMOTOPY EQ

[5]

Baum P., 1994, Contemp. Math., V167, P240, DOI 10.1090/conm/167/1292018

[6]

Blackadar B., 1986, MATH SCI RES I PUBLI, V5

[7]

BLANCHARD E, 1993, THESIS U PARIS 7

[8]

BOURBAKI N, 1960, TOPOLOGIE GEN

[9] CYCLIC COHOMOLOGY, THE NOVIKOV-CONJECTURE AND HYPERBOLIC GROUPS [J].

CONNES, A ;

MOSCOVICI, H .

TOPOLOGY, 1990, 29 (03) :345-388

[10] THE LONGITUDINAL INDEX THEOREM FOR FOLIATIONS [J].

CONNES, A ;

SKANDALIS, G .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1984, 20 (06) :1139-1183

← 1 2 3 →