Large Riemannian manifolds which are flexible

• 成果类型: Article
• 署名作者: Dranishnikov, AN; Ferry, SC; Weinberger, S
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2003.157.919
• 发表日期: 2003
• 页码: 919-938
• 关键词: baum-connes conjecture

摘要

For each k is an element of Z, we construct a uniformly contractible metric on Euclidean space which is not mod k hypereuclidean. We also construct a pair of uniformly contractible Riemannian metrics on R-n, n greater than or equal to 11, so that the resulting manifolds Z and Z' are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism. We show that for these spaces the C*-algebra assembly map K-*(lf) (Z) --> K-* (C* (Z)) from locally finite K-homology to the K-theory of the bounded propagation algebra is not a monomorphism. This shows that an integral version of the coarse Novikov conjecture fails for real operator algebras. If we allow a single cone-like singularity, a similar construction yields a counterexample for complex C*-algebras.