Except, instead of rock and roll music, my concert was a lecture on black hole topology.

除了我排队不是摇滚乐，我演唱会是黑洞拓扑学讲座。

Topology was originally studied as a branch of purely abstract mathematics.

拓扑学最初是作为纯抽象数学一来研究。

First of all, topology is a branch of mathematics that focuses on fundamental properties of objects.

首先， 拓扑学是数学一，侧重于对象基本属性。

This involved lots of weird quantum phenomena, plus a branch of math called topology, which looks at how objects can be arranged and manipulated.

这包括许多奇特量子现象与数学中一称为拓扑学，拓扑学关注是物体可如何被排列与操纵。

A donut and a coffee cup look the same to a topologist because they both have one hole.

一和一咖啡杯在拓扑学家看来是一样，因为它们都有一洞。

For a long time, it wasn't clear whether topology was useful for describing the behaviors of subatomic particles.

长期以来，人们并不清楚拓扑学是否有助于描述亚原子粒子行为。

Thouless and the final winner, Duncan Haldane, are both also using topology to pave the way for a new kind of material: topological insulators.

索利斯及最后一位获奖者邓肯·霍尔丹都用拓扑学为一种新物质——拓扑绝缘体开辟了道路。

This powerful result is a cornerstone of topology, a branch of mathematics concerned with the fundamental properties of space, significantly impacting fields ranging from data science to physics.

这一强有力结果是拓扑学基石，拓扑学是与空间基本属性有关数学，对从数据科学到物理学等领域产生了重大影响。

In topology since one block of buildings surrounded by roads is considered equivalent, settlements with a wide range of shapes and sizes, from the suburbs of Las Vegas to the slums of Mumbai, can be analyzed in the same way.

在拓扑学中，由于被道路包围一栋建筑物被认为是等效，从拉斯维加斯郊区到孟买贫民窟各种形状和大小定居点，可以以相同方式进行析。