# 401-3180-20L Introduction to Homotopy Theory and Model Category Structure

Semester | Spring Semester 2020 |

Lecturers | J. Ducoulombier |

Periodicity | non-recurring course |

Language of instruction | English |

Comment | Number of participants limited to 24. |

### Courses

Number | Title | Hours | Lecturers | ||||
---|---|---|---|---|---|---|---|

401-3180-20 S | Introduction to Homotopy Theory and Model Category Structure | 2 hrs |
| J. Ducoulombier |

### Catalogue data

Abstract | Introductory seminar about category theory and techniques in Algebraic topology such as model category structure and "homotopy" limits and colimits. |

Learning objective | It is well known that topological spaces are endowed with a homotopy theory classifying objects up to continuous deformations. Model categories provide a natural setting for homotopy theory and it has been used in some parts of algebraic K-theory, algebraic geometry and algebraic topology, where homotopy-theoretic approaches led to deep results. The goal of this seminar is to get an introduction to model structures through examples (topological spaces, simplicial sets, chains complexes...). To get further into this theory, we develop the notion of derived functors with applications to homotopy limits and colimits. |

Literature | "Homotopy theories and model categories" Dwyer and Spalinski "A primer on homotopy colimits" Dugger "Model categories" Hovey |

Prerequisites / Notice | The students are expected to be familiar with topological spaces and fundamental groups. This seminar takes the form of a working group, where interactions are encouraged. Participants are expected to attend the seminar, give a presentation and write a report. Topic will be assigned during the first meeting. |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 4 credits |

Examiners | J. Ducoulombier |

Type | ungraded semester performance |

Language of examination | English |

Repetition | Repetition only possible after re-enrolling for the course unit. |

Additional information on mode of examination | Participants are expected to attend the seminar, give a presentation and write a report. |

### Learning materials

No public learning materials available. | |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

Places | Limited number of places. Special selection procedure. |

Beginning of registration period | Registration possible from 06.01.2020 |

Priority | Registration for the course unit is only possible for the primary target group |

Primary target group | Mathematics BSc (404000)
starting semester 05 Mathematics MSc (437000) Applied Mathematics MSc (437100) |

Waiting list | until 18.02.2020 |

End of registration period | Registration only possible until 12.02.2020 |

### Offered in

Programme | Section | Type | |
---|---|---|---|

Mathematics Bachelor | Seminars | W | |

Mathematics Master | Seminars | W |