奇阶阿贝尔基本群流形上的正标量曲率

IF 2 1区数学

Geometry & Topology Pub Date : 2019-08-02 DOI:10.2140/GT.2021.25.497

B. Hanke

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引用次数: 5

摘要

在具有Baas-Sullivan奇点的流形上引入了正标量曲率的黎曼度量，证明了相应的同调不变性原理，并讨论了可容许积。利用这一理论，我们在至少五维的闭光滑流形上构造了正标量曲率度量，这些流形具有奇阶阿贝尔基本群，是非自旋的和非自旋的。本文解决了一类具有有限基本群的流形的Gromov-Lawson-Rosenberg猜想。

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Positive scalar curvature on manifolds with odd order abelian fundamental groups

We introduce Riemannian metrics of positive scalar curvature on manifolds with Baas-Sullivan singularities, prove a corresponding homology invariance principle and discuss admissible products. Using this theory we construct positive scalar curvature metrics on closed smooth manifolds of dimension at least five which have odd order abelian fundamental groups, are non-spin and atoral. This solves the Gromov-Lawson-Rosenberg conjecture for a new class of manifolds with finite fundamental groups.

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来源期刊

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.