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

除了我排队的不是摇滚乐，我的演唱会是黑洞拓扑学的讲座。

So that's the concept of retinotopy or the map in visual cortex.

这就是视网膜拓扑学或视觉皮层中的地图的概念。

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

首先， 拓扑学是数学的分支，侧重于对象的基本属性。

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

这包括许多奇特的量子现象数学中称为拓扑学的分支，拓扑学关注的是物体可如何被排列操纵。

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

拓扑学最初是作为纯抽象数学的分支来研究的。

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

甜甜圈咖啡杯在拓扑学家看来是样的，因为它们都有洞。

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

长期以来，们并不清楚拓扑学是否有助于描述亚原子粒子的行为。

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

索利斯及最后位的获奖者邓肯·霍尔丹都用拓扑学为种新物质——拓扑绝缘体开辟了道路。

Topologists do this when the count the holes in a surface, physicists do this in defining the ideas of energy and momentum, or in special relativity when they define proper time.

拓扑学家在计算表面上的孔洞时这样做，物理学家在定义能量动量的概念时这样做，或者在狭义相对论中定义适当的时间时这样做。

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，由于被道路包围的栋建筑物被认为是等效的，从拉斯维加斯郊区到孟买贫民窟的各种形状小的定居点，可以以相同的方式进行分析。