相对论中几何与拓扑的另一种框架
An Alternative Framework of Geometry and Topology in Relativity
摘要：
我们研究几何和拓扑作为数学空间的互补和对偶方面。同样的方法也可以用来更好地理解宇宙学常数。到目前为止，我们还没有把引力和其他三种基本规范力纳入一个适当的统一框架，现在我们面临着一个额外的不需要的第五种排斥力，也被设想为暗能量问题。如何理解这种3+1+1基本力困境？我们在这里介绍一个关于基本力的新概念。这将给我们一个额外的和包罗万象的方式来分类这五个基本力在一个一致的方式，从而加强几何拓扑互补的概念。这也有助于我们理解，在广义相对论中，当用最后一个术语“小”来代替${g_{μν}} = {η_{μν}} + {h_{μν}}$时，实际上意味着什么。这提供了对几何和拓扑结构的类属关系和互补性的理解，然后将其形式化为基本定理，使我们能够理解物理现实和纯数学结构之间的潜在联系。
英文摘要：
We study geometry and topology as complementary and dual aspects of the mathematical space. The same is used to get a better understanding of the Cosmological Constant. Having failed so far to include gravity in a proper unified framework with the other three fundamental gauge forces, we are now faced with an additional unwanted fifth force of repulsion, also envisaged as the Dark Energy problem. How does one understand this 3+1+1 fundamental force dilemma? We introduce here a novel idea of the Fundamental Forces. This will give us an additional and an all-encompassing way of classifying these five fundamental forces in a consistent manner and thereby strengthen the geometry-topology complementarity concept. This also helps us to understand as to what one actually means when substituting ${g_{μν}} = {η_{μν}} + {h_{μν}}$ with the last term being "small" in General Relativity. This provides an understanding of the generic relationship and the complementarity of the geometric and the topological structures which is then formalized as a basic theorem enabling us to understand the underlying connection between the physical reality and the pure mathematical structures.
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。
