Lipschitz上同调、Novikov猜想和展开式
Lipschitz Cohomology, Novikov conjecture, and Expanders
摘要：
本文给出了闭非球面流形的上同调是Connes-Gromov-Moscovici [CGM]意义下的真Lipschitz的充分条件.这些条件用流形的泛覆盖的斯通-切赫紧化来表示.我们证明了这些条件在形式上弱于[CP]中给出的Novikov猜想成立的充分条件.证明了具有适当Lipschitz上同调的闭非球面流形的基本群的Cayley图不可能包含一个粗略意义下的扩张子。特别是，这排除了Lipschitz上同调方法的诺维科夫猜想最近格罗莫夫的例子，异国情调的群体。
英文摘要：
We present sufficient conditions for the cohomology of a closed aspherical manifold to be proper Lipschitz in sense of Connes-Gromov-Moscovici [CGM]. The conditions are stated in terms of the Stone-Čech compactification of the universal cover of a manifold. We show that these conditions are formally weaker than the sufficient conditions for the Novikov conjecture given in [CP]. Also we show that the Cayley graph of the fundamental group of a closed aspherical manifold with proper Lipschitz cohomology cannot contain an expander in the coarse sense. In particular, this rules out a Lipschitz cohomology approach to the Novikov Conjecture for recent Gromov's examples of exotic groups.
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