# Abelianizations of mapping class groups

Specialeforsvar: Jan McGarry Furriol

Titel: Abelianizations of mapping class groups

Abstract: We study the application by Galatius and Randal-Williams of their work on homology of moduli spaces of manifolds to the calculation of abelianizations of the mapping class groups of the manifolds $W^{2n}_{g}=\#^{g}(S^{n}\times S^{n})$ for $n\ge 3$ and $g\ge5$. We use the same approach to carry out these calculations for smooth hypersurfaces of $\CP^{4}$; the result is that the abelianizations of their mapping class groups is trivial.

Vejleder: Søren Galatius
Censor:    Iver Mølgaard Ottosen, DTU