Boundary Dehn twists are often commutators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913168567042048 |
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| author | Lindblad, Ayodeji |
| author_facet | Lindblad, Ayodeji |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundary Dehn twists are often commutators Lindblad, Ayodeji Geometric Topology 57R50 (primary), 57R52, 57K40, 57S05, 14M10 (secondary) 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. |
| title | Boundary Dehn twists are often commutators |
| topic | Geometric Topology 57R50 (primary), 57R52, 57K40, 57S05, 14M10 (secondary) |
| url | https://arxiv.org/abs/2604.13194 |