堤 幸博 (慶應義塾大学, 日本学術振興会特別研究員(PD))
タイトル：A surgery description of homology solid tori and its applications to the Casson invariant

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アブストラクト：
It is known that every homology solid torus can be obtained from the standard solid torus $D^2 \times S^1$ by surgery on a suitable boundary link. In particular, every knot $K$ in $S^3$ has a surgery description $(k; (k_i,e_i)_{i=1,2,...,m})$, where $k$ is a trivial knot, $(k_i,e_i)$ is an $e_i$-framed knot in $S^3 - k$ with $e_i = \pm 1$, which satisfies the following properties:
\begin{itemize}
\item
$k_1$, \ldots, $k_m$ bound mutually disjoint genus one Seifert surfaces $S_1$, \ldots, $S_m$ in $S^3 - k$,
\item
there non-separating simple closed curves $x_i$, $y_i$ on each $S_i$ such that
\begin{itemize}
\item
$x_i$ intersects $y_i$ transversely in a single point,
\item
$x_i$ bounds a disk $D_i$ with $D_i \cap S_i = \partial D_i = x_i$ which meets $k$ in a single point,
\item
the linking number ${\rm lk}(y_i,k)=0$.
\end{itemize}
\item
$a_2(K) = -\sum^m_{i=1} e_i {\rm lk} (y_i, y^+_i)$.
\end{itemize}
Using such a surgery description for $K$, we study the relation between the Alexander invariant of $K$ and the Casson-Walker-Lescop invariant of the cyclic covering spaces of $S^3$ branched along $K$.