标题： 如何从小的异胚 R^4 获得宇宙常数 显示英文标题

标题： How to obtain a cosmological constant from small exotic R^4

摘要： 本文中，我们通过应用某些低维微分拓扑技术，将宇宙学常数确定为一个拓扑不变量。 我们处理了一个嵌入到标准 $\mathbb{R}^{4}$ 中的小的异胚 $R^{4}$。 任何异胚 $R^4$ 都是一个黎曼可微流形，并且其曲率张量必然非零。 为了确定此类曲率的不变部分，我们处理了 $R^4$ 的一种规范构造，在其中它作为复曲面 $K3\#\overline{CP(2)}$ 的一部分出现。 这种 $R^{4}$ 承载双曲几何。 这一事实显著简化了计算，并加强了表达式的刚性。 特别是，我们用一个由（自然）拓扑不变量组合而成的值来解释宇宙学常数的小值。 最后，宇宙学常数似乎是一个由拓扑支持的量。 显示英文摘要

摘要： In this paper we determine the cosmological constant as a topological invariant by applying certain techniques from low dimensional differential topology. We work with a small exotic $R^{4}$ which is embedded into the standard $\mathbb{R}^{4}$. Any exotic $R^4$ is a Riemannian smooth manifold with necessary non-vanishing curvature tensor. To determine the invariant part of such curvature we deal with a canonical construction of $R^4$ where it appears as a part of the complex surface $K3\#\overline{CP(2)}$. Such $R^{4}$'s admit hyperbolic geometry. This fact simplifies significantly the calculations and enforces the rigidity of the expressions. In particular, we explain the smallness of the cosmological constant with a value consisting of a combination of (natural) topological invariant. Finally, the cosmological constant appears to be a topologically supported quantity.