On four-dimensional Dehn twists and Milnor fibrations

Hokuto Konno; Jianfeng Lin; Anubhav Mukherjee; Juan Muñoz-Echániz

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arXiv · 2409.11961

On four-dimensional Dehn twists and Milnor fibrations

Hokuto Konno·Jianfeng Lin·Anubhav Mukherjee·Juan Muñoz-Echániz

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Abstract

We study the monodromy diffeomorphism of Milnor fibrations of isolated complex surface singularities, by computing the family Seiberg--Witten invariant of Seifert-fibered Dehn twists using recent advances in monopole Floer homology. More precisely, we establish infinite order non-triviality results for boundary Dehn twists on indefinite symplectic fillings of links of minimally elliptic surface singularities. Using this, we exhibit a wide variety of new phenomena in dimension four: (1) smoothings of isolated complex surface singularities whose Milnor fibration has monodromy with infinite order as a diffeomorphism but with finite order as a homeomorphism, (2) robust Torelli symplectomorphisms that do not factor as products of Dehn--Seidel twists, (3) compactly supported exotic diffeomorphisms of exotic $\mathbb{R}^4$'s and contractible manifolds.

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BibTeX RIS

Hokuto Konno, Jianfeng Lin, Anubhav Mukherjee, Juan Muñoz-Echániz. 2024-09-18. On four-dimensional Dehn twists and Milnor fibrations. https://arxiv.org/abs/2409.11961

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