Graph complexes are chain complexes with very simple descriptions in terms of finite graphs. They were introduced by Kontsevich in his work on deformation quantization, in particular in the proof of his “formality theorem,” but have proved to have applications in a wide variety of other areas. These include the study of groups important in low-dimensional topology such as automorphism groups of free groups and surface mapping class groups. This course will be an introduction to these complexes, with special emphasis on their applications in geometric group theory.
|Lecture 1||Introduction, oriented graphs, (cyclic) operads||TCC Lec 1||Lecture 1|