标题： 全息原理的拓扑起源：虫洞的应用 显示英文标题

标题： Topological Origin of Holographic Principle: Application to wormholes

摘要： 在本文中，我们通过拓扑收缩理论提出了全息原理的数学表示。 我们发现拓扑收缩是现代量子引力中全息思想的数学类比，并可用于探索全息边界几何。 给出了五维（5D）虫洞时空$W$的一个例子，我们发现它可以收缩到低维圆圈$S_i \subset W$。 根据全息原理，该时空体积$W$的描述被编码在作为区域边界的低维圆圈上。 显示英文摘要

摘要： In this paper, we suggest a mathematical representation to the holographic principle through the theory topological retracts. We found that the topological retraction is the mathematical analogs of the hologram idea in modern quantum gravity and it can be used to explore the geometry of the hologram boundary. An example has been given on the five dimensional (5D) wormhole space-time $W$ which we found it can retract to lower dimensional circles $S_i \subset W$. In terms of the holographic principle, the description of this volume of space-time $W$ is encoded on the lower-dimensional circle which is the region boundary.