Rational homology disk smoothings and Lefschetz fibrations

Abstract

In this article, we generalize the results discussed in [arXiv:1004.3762] 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.

arXiv comment25 pages, 39 Figures, To appear in J. Korean Math. Soc