【摘要】
In recent years,there have been several breakthroughs in understanding diffeomorphism groups and mapping class groups of 4-manifolds, using techniques related to configuration spaces.In this lecture series,I will talk about three invariants from configuration spaces: the Dax invariant,the w3 invariant (defined by Budney-Gabai), and the 4-dimensional Kontsevich integral (computed by Watanabe).I will give explicit constructions of (families of) diffeomorphisms on simple 4-manifolds (including S4, S1 cross S3, surface products and hyperbolic 4-manifolds) and detect them using these invariants. In particular, this shows that topological properties of diffeomorphism groups of simple 4-manifolds are usually very complicated.
