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J. Korean Math. Soc. 2023; 60(1): 227-253

Online first article December 14, 2022      Printed January 1, 2023

https://doi.org/10.4134/JKMS.j220363

Copyright © The Korean Mathematical Society.

Rational homology disk smoothings and Lefschetz fibrations

Hakho Choi

Seoul National University

Abstract

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In this article, we generalize the results discussed in \cite{MR2783383} by introducing a genus to generic fibers of Lefschetz fibrations. That is, we give families of relations in the mapping class groups of genus-1 surfaces with boundaries that represent rational homology disk smoothings of weighted homogeneous surface singularities whose resolution graphs are $3$-legged with a bad central vertex.

Keywords: Lefschetz fibration, rational homology disk smoothing, rational blowdowns

MSC numbers: 57K43, 53D05, 14J17

Supported by: The author is supported by a KIAS Individual Grant (MG071002) at Korea Institute for Advanced Study.

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