A note on the boundary Dehn twist of K3 surfaces

2025/06/12 by Yujie Lin, Lin, Yujie
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2506.10444

openalex publication_date 2025/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Spin^ℂ families due to Baraglia-Konno and the global Torelli theorem of K3 surfaces.

Citations

• Irreducible 4-manifolds can admit exotic diffeomorphisms
• Mapping class groups of simply connected 4-manifolds with boundary
• On Torelli groups and Dehn twists of smooth 4-manifolds
• The Dehn twist on a sum of two K3 surfaces
• The stable mapping class group of simply connected 4-manifolds

Related

• The Boundary Dehn Twist on a Punctured Connected Sum of Two K3 Surfaces is Nontrivial in the Smooth Mapping Class Group
• An algebraic characterization of a Dehn twist for nonorientable surfaces
• The generalized Dehn twist along a figure eight
• On Torelli groups and Dehn twists of smooth 4-manifolds
• The Dehn twist coefficient for big and small mapping class groups