کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4592102 1335074 2008 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An equivariant higher index theory and nonpositively curved manifolds
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
An equivariant higher index theory and nonpositively curved manifolds
چکیده انگلیسی

In this paper, we define an equivariant higher index map from to K∗(C∗Γ(X)) if a torsion-free discrete group Γ acts on a manifold X properly, where C∗Γ(X) is the norm closure of all locally compact, Γ-invariant operators with finite propagation. When Γ acts on X properly and cocompactly, this equivariant higher index map coincides with the Baum–Connes map [P. Baum, A. Connes, K-theory for discrete groups, in: D. Evens, M. Takesaki (Eds.), Operator Algebras and Applications, Cambridge Univ. Press, Cambridge, 1989, pp. 1–20; P. Baum, A. Connes, N. Higson, Classifying space for proper actions and K-theory of group C∗-algebras, in: C∗-Algebras: 1943–1993, San Antonio, TX, 1993, in: Contemp. Math., vol. 167, Amer. Math. Soc., Providence, RI, 1994, pp. 240–291]. When Γ is trivial, this equivariant higher index map is the coarse Baum–Connes map [J. Roe, Coarse cohomology and index theory on complete Riemannian manifolds, Mem. Amer. Math. Soc. 104 (497) (1993); J. Roe, Index Theory, Coarse Geometry, and the Topology of Manifolds, CBMS Reg. Conf. Ser. Math., vol. 90, Amer. Math. Soc., Providence, RI, 1996]. If X is a simply-connected complete Riemannian manifold with nonpositive sectional curvature and Γ is a torsion-free discrete group acting on X properly and isometrically, we prove that the equivariant higher index map is injective.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 255, Issue 6, 15 September 2008, Pages 1480-1496