涩里番

Title: The Euler class of big mapping class groups.

Abstract: For an orientable surface $S$ with a marked point $p$, the mapping class group $Mod(S,p)$ carries a canonical Euler class in its second cohomology group. Equivalently, this class is the Euler class of smooth orientable $S$-bundles with a chosen section. Using these two viewpoints, I will show that for many infinite-type surfaces $S$, the Euler class is nontrivial. Furthermore, I will discuss how the behavior of its powers depends on the genus and on the topology of the space of ends of the surface. This is joint work with Rita Jim茅nez and Israel Morales.

We will gather in the lounge for teatime after the talk.