Homology-genericity, horizontal Dehn surgeries and ubiquity of rational homology 3-spheres (Q2846758)

In the paper under review, it is shown that horizontal Dehn surgeries along a set of simple closed curves on a Heegaard surface, each of which represents a ``generic'' homology class, yield a rational homology 3-sphere if the number of the curves is at least the genus of the Heegaard surface. Here ``generic'' means that the homology classes are much ``common'' in the set of curve-represented homology classes with respect to a canonical homological basis. Note that this result can be regarded as an alternative version of the theorem obtained by \textit{N. M. Dunfield} and \textit{W. P. Thurston} [Invent. Math. 166, No. 3, 457--521 (2006; Zbl 1111.57013)].