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

SemesterSpring Semester 2020
LecturersJ. Ducoulombier
Periodicitynon-recurring course
Language of instructionEnglish
CommentNumber of participants limited to 24.

AbstractIntroductory seminar about category theory and techniques in Algebraic topology such as model category structure and "homotopy" limits and colimits.
ObjectiveIt 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 / NoticeThe 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.