Topology of moduli spaces

数学对象的空间或某个固定对象的子空间的形成方法有很多种，研究这样的空间的拓扑通常是相当有趣的。例子是模空间的光滑流形，提供了一个新的视角研究的同构群，经典的例子，如配置空间及其变种，或空间的黎曼度量受曲率条件。同伦理论中越来越复杂的技术正被用来研究这样的空间。这个项目将部署这样的方法来调查的问题，如：不同的数学对象可以有等价的模空间？

There are many ways of forming spaces of mathematical objects, or of subobjects of some fixed one, and it is usually of considerable interest to examine the topology of such spaces. Examples are moduli spaces of smooth manifolds, giving a new perspective on the study of diffeomorphism groups, classical examples such as configuration spaces and their variants, or spaces of Riemannian metrics subject to curvature conditions. Increasingly sophisticated techniques from homotopy theory are being used to examine such spaces. This project will deploy such methods to investigate questions such as: can distinct mathematical objects have equivalent moduli spaces?