Exotic Dehn twists and homotopy coherent group actions

2024/09/18 by Sungkyung Kang, Kang, Sungkyung, JungHwan Park +3 · 4 citations
Mathematics · #57K41 #57R50 #57R85 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2409.11806

openalex publication_date 2024/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the question of extending a smooth homotopy coherent finite cyclic group action on the boundary of a smooth 4-manifold to its interior. As a result, we prove that Dehn twists along any Seifert homology sphere, except the 3-sphere, on their simply connected positive-definite fillings are infinite order exotic.

Cited by

• Non-kinetic homotopy coherent actions on four-manifolds
• The Boundary Dehn Twist on a Punctured Connected Sum of Two K3 Surfaces is Nontrivial in the Smooth Mapping Class Group
• Constraints on Lefschetz fibrations with four-dimensional fibers from Seiberg-Witten theory
• On absolutely exotic diffeomorphisms of 4-manifolds

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