English

Boundary Dehn twists are often commutators

Geometric Topology 2026-05-29 v2

Abstract

For XX 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,ca,c of punctured XX rel boundary whose commutator [a,c][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 K3K3 surface is trivial.

Keywords

Cite

@article{arxiv.2604.13194,
  title  = {Boundary Dehn twists are often commutators},
  author = {Ayodeji Lindblad},
  journal= {arXiv preprint arXiv:2604.13194},
  year   = {2026}
}

Comments

27 pages, 2 figures. Added new results, refined exposition. Comments welcome!

R2 v1 2026-07-01T12:09:36.594Z