Abstract

Abstract These lecture notes are mainly concerned with how the concept of topological insulators is generalized when interactions are included. More generally, the interplay of symmetry and topology is discussed. Traditionally, phases of matter were distinguished on the basis of symmetry alone. On the other hand, fractional quantum Hall phases are examples of topological states whose essential character does not require a discussion of symmetry. However, topological insulators are an example of a new phase of matter that combines both symmetry and topology.

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