Generalized infinite-order monodromy conjecture for surface singularity smoothings
Let be a normal isolated surface singularity with rational homology -sphere link, and let it have a smoothing with Milnor fiber and monodromy . Suppose that acts with finite order on . Let denote the geometric genus of the singularity. Generalized infinite-order monodromy conjecture. The monodromy has infinite order in the smooth mapping class group when . This generalizes the hypersurface case and is motivated by examples for equivariant smoothings of quasi-homogeneous minimally elliptic surface singularities; the proposition in the paper gives finite order in the topological mapping class group under the stated homological hypothesis, while the smooth assertion remains open.
References
Primary source
Hokuto Konno, Jianfeng Lin, Anubhav Mukherjee and Juan Muñoz-Echániz, “On four-dimensional Dehn twists and Milnor fibrations”, arXiv:2409.11961 (2024).
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