Kathryn Hess Bellwald #1/3

Abstract: In this mini-course I will introduce various simplicial, cosimplicial, and chain complex models for free loop spaces and their structure maps and describe the relationships among these models. 1. Simplicial and cosimplicial models * The cyclic nerve * The simplicial Hochschild construction * The simplicial coHochschild construction * The cocyclic model of Jones 2. Chain complex models * Preliminaries on the bar and cobar constructions * The Hochschild complex * The coHochschild complex * The cyclic complex * The cocyclic complex * Hochschild cohomology