The Boundary Dehn Twists on Punctured K3 Surfaces

G2T2 Seminar

Organizers：

G2T2 Group

The G2T2 (Geometry, Group Theory, Topology) seminar is a seminar run (predominantly) by postdocs and students, with (predominantly) postdoc and student speakers. The organisers (in alphabetical order) consist of: Yifei CAI 蔡逸飞, Xiao CHEN 陈啸, Diptaishik CHOUDHURY, Qiliang LUO 罗琪亮, Tuo SUN 孙拓, Ivan TELPUKHOVSKIY, and Daxun WANG 王大洵 (*).

Speaker：

YuJie LIN 林毓杰 (THU)

Time：

Fri., 10:00-11:30 am, Oct. 31, 2025

Venue：

Ningzhai (宁斋) 203

Title:

The Boundary Dehn Twists on Punctured K3 Surfaces

Abstract:

In 4-manifold topology, Dehn twists along Seifert fibered 3-manifolds provide an important source fof exotic diffeomorphisms. A notable example is the boundary Dehn twist on a punctured K3 surface, which Baraglia-Konno and Kronheimer-Mrowka proved is nontrivial in the smooth mapping class group relative to boundary. I will show that despite being smoothly nontrivial, this diffeomorphism is trivial in the abelianization of the mapping class group. The proof is based on an obstruction for Spin^\mathbb{C} families due to Baraglia-Konno and the global Torelli theorem of K3 surfaces.