Teruhisa Kadokami (OCAMI, Osaka City University)
Title: How to use the Reidemeister torsion
Abstract:
Firstly, we give the definition of the Reidemeister torsion,
and explain basic properties, following V.~G.~Turaev.
Secondly, we consider the Reidemeister torsion of a homology lens space,
which is the result of $p/q$-surgery along a knot $K$ in a homology
$3$-sphere $\Sigma$.
We denote the homology lens space by $\Sigma (K;p/q)$.
Main Theorem 1 is the case that $K$ is a torus knot in $S^3$.
Main Theorem 2 is the case that the Alexander polynomial of $K$,
${\mit \Delta}_K(t)$, is degree 2.
We judge when the homology lens spaces are homeomorphic
to lens spaces by using the Reidemeister torsion.