标题： 粗拓扑的灯夫简介 显示英文标题

标题： An illustrated introduction to the coarse topology of lamplighters

摘要： 大致来说，灯工图编码了灯工沿着给定图移动并在顶点处修改灯颜色的可能配置。 本文致力于以下微妙的问题：两个灯工图何时具有相同的粗几何结构，即它们何时是拟等距的？ 受到来自拓扑学的一些基本思想的启发，我们将对其进行“粗化”，我将概述一些技术，这些技术允许我们有效地比较灯工图（以及更多内容）在拟等距意义上的差异。 基于2025年8月在傅里叶研究所举行的几何拓扑日上讲授的一个短期课程。 显示英文摘要

摘要： Roughly speaking, lamplighter graphs encode the possible configurations of a lamplighter that moves along a given graph and that modifies the colours of lamps at vertices. This article is dedicated to the following delicate question: when do two lamplighter graphs have the same coarse geometry, i.e.\ when are they quasi-isometric? Inspired by elementary ideas from topology, which we will ``coarsify'', I will survey some techniques that allow us to compare efficiently lamplighter graphs (and more) up to quasi-isometry. Based on a minicourse given during the Journ\'ees de Topologie G\'eom\'etrique at the Institut Fourier in August 2025.