Nielsen realization problem for del Pezzo surfaces
Nielsen realization problem for del Pezzo surfaces

Seraphina Lee, University of Chicago
Fine Hall 314
The (cyclic) Nielsen realization problem for a closed, oriented manifold asks whether any mapping class of finite order m can be represented by a homeomorphism of order m. In this talk I will discuss two results about the Nielsen realization problem for del Pezzo surfaces M^4. First, I will explain a classification of order2 elements of the topological mapping class group Mod(M^4) and deduce the realizability of order2 mapping classes by diffeomorphisms. I will also discuss joint work in progress with Tudur Lewis and Sidhanth Raman comparing the smooth, complex, and metric versions of the Nielsen realization problem for certain ("irreducible'') finiteorder elements of Mod(M^4).