A notion of geometric complexity and its application to topological rigidity

• 成果类型: Article
• 署名作者: Guentner, Erik; Tessera, Romain; Yu, Guoliang
• 署名单位: Vanderbilt University; University of Hawaii System; University of Hawaii Manoa
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0366-z
• 发表日期: 2012
• 页码: 315-357
• 关键词: novikov-conjecture; asymptotic dimension; linear-groups; K-THEORY; MANIFOLDS

摘要

We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is homotopy equivalent to M, then Mxae (n) is homeomorphic to Nxae (n) , for n large enough. This statement is known as the stable Borel conjecture. On the other hand, we show that the class of FDC groups includes all countable subgroups of GL(n,K), for any field K.