On four-dimensional Dehn twists and Milnor fibrations

Autor:	Konno, Hokuto, Lin, Jianfeng, Mukherjee, Anubhav, Muñoz-Echániz, Juan
Rok vydání:	2024
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Geometry Mathematics - Differential Geometry Mathematics - Symplectic Geometry 57K41 57R58
Druh dokumentu:	Working Paper
Popis:	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. Comment: 72 pages. Comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.11961 Zobrazit plný text záznamu View this record from Arxiv