分类映射的上核引起的正数量曲率
Positive Scalar Curvature due to the Cokernel of the Classifying Map
摘要：
本文对正数量曲率度量的协边性和协整性进行了分类。设$M$是一个维数为$\ge 5$的闭自旋流形，它允许一个度量具有正的数量曲率.本文给出了$M$上psc度量群的秩的下界，直到标准映射$KO_*(M)\to KO_*(Bπ_1(M))$的corank，只要有理解析Novikov猜想对$π_1(M)$成立.
英文摘要：
This paper contributes to the classification of positive scalar curvature metrics up to bordism and up to concordance. Let $M$ be a closed spin manifold of dimension $\ge 5$ which admits a metric with positive scalar curvature. We give lower bounds on the rank of the group of psc metrics over $M$ up to bordism in terms of the corank of the canonical map $KO_*(M)\to KO_*(Bπ_1(M))$, provided the rational analytic Novikov conjecture is true for $π_1(M)$.
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