Gromov正数量曲率猜想与有理非本质宏观大流形
Gromov positive scalar curvature conjecture and rationally inessential macroscopically large manifolds
摘要：
我们给出了第一个合理的非本质的，但宏观大流形的例子。我们的流形是Dranishnikov合理性猜想的反例。对于其中的一些，我们证明了它们不允许正数量曲率度量，从而满足Gromov正数量曲率猜想.流形的基本群是直角Coxeter群的有限指数子群。该结构使用小的覆盖凸多面体（或替代戴维斯复杂）和手术。
英文摘要：
We give the first examples of rationally inessential but macroscopically large manifolds. Our manifolds are counterexamples to the Dranishnikov rationality conjecture. For some of them we prove that they do not admit a metric of positive scalar curvature, thus satisfy the Gromov positive scalar curvature conjecture. Fundamental groups of our manifolds are finite index subgroups of right angled Coxeter groups. The construction uses small covers of convex polyhedrons (or alternatively Davis complexes) and surgery.
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