Introduction to dendroidal topology. Part 1 of 4

Dendroidal topology is an extension of simplical topology, geared towards the theory of operads and of infinity-operads. In the first part of the course, we will discuss topological operads and their algebras, and the Boardman-Vogt resolution. Next, we will introduce the category of dendroidal sets, and the corresponding notion of infinity operad. This will naturally include a discussion of the Joyal model structure on simplicial sets and the corresponding notion of infinity category. We will discuss several models for the homotopy theory of dendroidal sets, e.g. the one based on dendroidal complete Segal spaces, and conclude with the relation between dendroidal sets and infinite loop spaces.

Prerequisites: The first two lectures should be accessible to anybody with basic knowledge of algebra, topology and category theory. The second part of the course will be harder to follow without familiarity with simplicial sets and some acquaintance with the notion of Quillen model category.