On the realizable topology of a manifold with attractors of geodesics

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• 作者：Marcio Colombo Fenille ^{mcfenille@gmail.com}
• 关键词：Algebraic and differential topology ; Riemannian manifolds ; General relativity
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：Complete
• 页码：158-168
• 全文大小：452 K
• 卷排序：111

文摘

We discuss the so-called realizable topology of a Riemannian manifold with attractors of geodesics, which we understand as its topological properties, mainly that related to its fundamental group, investigated from a viewpoint that may be considered realizable in a sense. In the special approach in which the manifold is understood as a model physical universe, we conclude that its realizable fundamental group is isomorphic to the classical fundamental group of its observable portion. For a universe of dimension at least three whose unobservable components are all contractible, this conclusion ensures the possibility to get real inferences about its classical fundamental group through observational methods.