Abstract
AbstractWe study lens space surgeries along two different families of 2-component links, denoted by${A}_{m, n} $and${B}_{p, q} $, related with the rational homology$4$-ball used in J. Park’s (generalized) rational blow down. We determine which coefficient$r$of the knotted component of the link yields a lens space by Dehn surgery. The link${A}_{m, n} $yields a lens space only by the known surgery with$r= mn$and unexpectedly with$r= 7$for$(m, n)= (2, 3)$. On the other hand,${B}_{p, q} $yields a lens space by infinitely many$r$. Our main tool for the proof are the Reidemeister-Turaev torsions, that is, Reidemeister torsions with combinatorial Euler structures. Our results can be extended to the links whose Alexander polynomials are same as those of${A}_{m, n} $and${B}_{p, q} $.
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