A note that we have written:
Domenico Fiorenza, Urs Schreiber, Alessandro Valentino,
Central extensions of mapping class groups from characteristic classes
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Volume LIX-3, 3ème trimestre 2018
on higher extensions of diffeomorphism groups and central extensions of mapping class groups induced by characteristic classes. This is part of the higher modularity of Local prequantum field theory.
We consider higher extensions of diffeomorphism groups and show how these naturally arise as the group stacks of automorphisms of manifolds that are equipped with higher degree topological structures, such as those appearing in topological field theories. Passing to the groups of connected components, we obtain abelian extensions of mapping class groups and investigate when they are central. As a special case, we obtain in a natural way the $\mathbb{Z}$-central extension needed for the anomaly cancellation of 3d Chern-Simons theory.
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