Novikov Conjectures, Index Theorems and Rigidity
Novikov Conjectures, Index Theorems and Rigidity
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DOI：
10.1017/cbo9780511629365
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
S. Ferry;A. Ranicki;Jonathan Rosenberg
中科院分区：
文献类型：
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作者：
S. Ferry;A. Ranicki;Jonathan Rosenberg
这是一篇说明性论文，解释了诺维科夫猜想的粗略类比，并描述了如何从中导出有关原始诺维科夫猜想的信息。例如，我们将解释诺维科夫关于有理蓬特里亚金类拓扑不变性的定理如何是粗略定理（其证明我们在附录中概述）的结果，而粗略定理反过来也暗示了非正弯曲流形的诺维科夫猜想。我们还对该技术进行了形式化，以便它可以应用于各种其他环境。因此，除了一些纯几何结果之外，我们还讨论了更高签名问题的等变、A 理论、分层和叶化版本。密切相关的论文有 [GL]、[CGM]、[CP]、[KaS]、[HR]、[Hu]。另请参阅调查 [We1]、[FRW]，了解更广泛的视角。
This is an expository paper explaining coarse analogues of the Novikov Conjecture and describing how information on the original Novikov Conjecture can be derived from these. For instance, we will explain how Novikov’s theorem on the topological invariance of rational Pontrjagin classes is a consequence of a coarse theorem (whose proof we sketch in an appendix) that in turn also implies the Novikov Conjecture for nonpositively curved manifolds. We also formalize the technique so that it can be applied in a wide variety of other contexts. Thus, besides a few purely geometric results, we also discuss equivariant, A-theoretic, stratified, and foliated versions of the higher signature problem. Closely related papers are [GL], [CGM], [CP], [KaS], [HR], [Hu]. See also the surveys [We1], [FRW], for wider perspectives.