HyperEuclidean流形与Novikov猜想
HyperEuclidean manifolds and the Novikov Conjecture
摘要：
我们发展了一些基本的Lipschitz同伦技巧，并将其应用于有限渐近维数的流形。特别地，我们证明了在有限维情形下，一致可缩流形的Higson紧化是mod $p$非循环的.然后给出了有限渐近维数群的高阶签名Novikov猜想的另一种证明。最后，我们定义了一个渐近分段欧氏度量空间，它是一个允许欧氏渐近多面体逼近的空间。证明了Gromov-Lawson猜想对渐近分段欧氏群成立。证明了扩张子不是渐近分段欧氏的
英文摘要：
We develop some basic Lipschitz homotopy technique and apply it to manifolds with finite asymptotic dimension. In particular we show that the Higson compactification of a uniformly contractible manifold is mod $p$ acyclic in the finite dimensional case. Then we give an alternative proof of the Higher Signature Novikov Conjecture for the groups with finite asymptotic dimension. Finally we define an asymptotically piecewise Euclidean metric space as a space which admits an approximation by Euclidean asymptotic polyhedra. We show that the Gromov-Lawson conjecture holds for the asymptotically piecewise Euclidean groups. Also we prove that expanders are not asymptotically piecewise Euclidean
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
