# Lecture notes and exercises

14 January 2019 | Lecture 1 |
Exercises in notes |
Automorphisms of free groups, history, models for F_n, Whitehead's algorithm |

28 January 2019 | Lecture 2 | Exercises in notes | Models for Outer space O_n and general O_{n,s}: sphere complexes and graphs. |

4 February 2019 | Lecture 3 | Exercises in notes | Contractibility of sphere complex and O_{n,s}, definition of spine K_{n,s} |

11 February 2019 | Lecture 4 | Exercises in notes | Applications of spine to finite subgroups, cohomological finiteness properties |

18 February 2019 | Lecture 5 | Exercises in notes | rational Euler characteristic of A_{n,s}, Homotopy type of links in K_{n,s} |

25 February 2019 | Lecture 6 | Exercises in notes | Homotopy type of links in K_{n,s} (contd.), A_{n,s}= Automorphisms of K_{n,s} |

4 March 2019 | Lecture 7 | Exercise in notes | A_{n,s}= Automorphisms of K_{n,s} (contd.), more on Euler characteristic, asymptotic expansions |

11 March 2019; | Lecture 8 | Exercise in notes Comments on notes |
Euler characteristic |

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