PrerequisiteAlgebraic TopologyAbstractThis course will discuss configuration spaces from the views of homotopy theory. The course will consist of three parts. In the first part, we will discuss the motivations of studying configuration spaces in homotopy theory, including the configuration space models for iterated loop spaces, little cube operads, and Hopf invariants. In the second part of the...
IntroductionIn this course, we introduce the general notion of (G,X)-structures on manifolds. After providing the basic results on the topology of surfaces (including the topological classification theorem), we will give a general panorama of (G,X)-structures in dimension two. We will focus on two classes of geometric structures:- metrics with constant curvature (possibly with singularities);- ...
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