Abstract:For $X$ any complete intersection of even complex dimension or any connected sum thereof (or, more generally, any space among certain broad classes of smooth manifolds), we concretely construct diffeomorphisms $a,c$ of punctured $X$ rel boundary whose commutator $[a,c]$ represents the smooth mapping class (rel boundary) of the boundary Dehn twist. This shows that boundary Dehn twists on 4-manifolds known to be nontrivial in the smooth mapping class group rel boundary by work of Baraglia-Konno, Kronheimer-Mrowka, J. Lin, and Tilton become trivial after abelianization, generalizing work of Y. Lin, who applied an argument based on the global Torelli theorem and an obstruction of Baraglia-Konno to prove that the abelianized boundary Dehn twist on the punctured $K3$ surface is trivial.
From: Ayodeji Lindblad [view email]
[v1]
Tue, 14 Apr 2026 18:17:03 UTC (222 KB)
[v2]
Wed, 27 May 2026 18:14:33 UTC (223 KB)
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