Asymptotic spectral flow for Dirac operators of disjoint Dehn twists

论四维Dehn扭转与Milnor纤维化

On four-dimensional Dehn twists and Milnor fibrations

该研究借助磁单极Floer同调进展计算族Seiberg--Witten不变量，证明极小椭圆奇点链不定辛填充的边界Dehn扭转无限阶非平凡，揭示了四维空间中三类全新的拓扑与辛几何现象。

The Dehn twist on a sum of two K3 surfaces

Ruberman gave the first examples of self-diffeomorphisms of four-manifolds that are isotopic to the identity in the topological category but not smoothly so. We give another example of this phenomenon, using the Dehn twist along a 3-sphere in the connected sum of two K3 surfaces.

Dehn扭转与自旋4维流形的Nielsen实现问题

Dehn twists and the Nielsen realization problem for spin 4-manifolds

本研究针对非零符号差的闭定向光滑自旋4维流形，证明围绕±2-球面的Dehn扭转不与有限阶微分同胚同伦，否定了相关映射类群的Nielsen实现问题，还发现K3与S²×S²连通和的拓扑与光滑范畴Nielsen实现问题存在差异，核心工具是Kato的对合10/8型不等式及其改进。

4-流形上的奇异Dehn扭

Exotic Dehn twists on 4-manifolds

该研究率先探索4-流形内沿非$S^3$ 3-流形的奇异Dehn扭，借助$\text{RP}^2$上的2参数族Seiberg-Witten理论，构造出多类新的奇异微分同胚例子，还证明了相关微分同胚群基本群同态的非满射性。

Constraints on Lefschetz fibrations with four-dimensional fibers from Seiberg-Witten theory

We establish constraints on the topology of smooth Lefschetz fibrations with $4$-dimensional fibers, by studying the family Bauer-Furuta invariant. To compute this invariant, we analyze the framed bordism class of 1-dimensional Seiberg-Witten moduli spaces using the local index theorem by Bismut-Freed. Using this, we deduce new obstructions to the smooth isotopy to the identity for compositions of Dehn twists on $(-2)$-spheres in closed $4$-manifolds. We obtain several applications: (1) We exhibit the first examples of closed simply-connected symplectic $4$-manifolds admitting Torelli symplect…