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.
关于四维 Dehn 扭转和 Milnor 纤度
我们利用单极浮子同调学的最新进展,通过计算塞弗特纤维德恩孪晶的塞伯格--威滕不变式族,研究了孤立复曲面奇点的米尔诺纤维的单旋转衍射。更确切地说,我们建立了最小椭圆曲面奇点链接的不定交映填充上边界 Dehn 扭曲的无穷阶非难性结果。利用这一点,我们展示了四维中的各种新现象:(1)孤立复曲面奇点的光滑化,其米尔诺纤维具有无穷阶的单漫射,但具有有限阶的同态;(2)不作为 Dehn--Seidel 扭转的乘积因子的稳健 Torellisymplectomorphisms;(3)奇异 $\mathbb{R}^4$'s 和可收缩流形的紧凑支撑奇异 diffeomorphisms。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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