A note on the boundary Dehn twist of K3 surfaces
Abstract
By the work of Baraglia-Konno and Kronheimer-Mrowka, the boundary Dehn twist on punctured K3 surfaces is nontrivial in the smooth mapping class group relative to boundary. In this short note, we prove that it becomes trivial after abelianization. The proof is based on an obstruction for SpinC families due to Baraglia-Konno and the global Torelli theorem of K3 surfaces.
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