Lens space surgeries along certain 2-component links related with Park's rational blow down, and Reidemeister-Turaev torsion
Teruhisa Kadokami, Yuichi Yamada

TL;DR
This paper classifies lens space surgeries along specific 2-component links related to rational blow downs, revealing new and unexpected surgery coefficients using Reidemeister-Turaev torsion techniques.
Contribution
It determines which Dehn surgery coefficients produce lens spaces for two families of links, including unexpected cases, and extends results via Alexander polynomial considerations.
Findings
$A_{m,n}$ yields lens spaces only at $r=mn$ and unexpectedly at $r=7$ for (2,3)
$B_{p,q}$ yields lens spaces for infinitely many $r$
Reidemeister-Turaev torsion is effective in classifying lens space surgeries
Abstract
We study lens space surgeries along two different families of 2-component links, denoted by and , related with the rational homology 4-ball used in J.\ Park's (generalized) rational blow down. We determine which coefficient of the knotted component of the link yields a lens space by Dehn surgery. The link yields a lens space only by the known surgery with and unexpectedly with for . On the other hand, yields a lens space by infinitely many . Our main tool for the proof is the Reidemeister-Turaev torsions, i.e.\ Reidemeister torsions with combinatorial Euler structures. Our results can be extended to the links whose Alexander polynomials are same with those of and .
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology
