通用不变量、康威多项式和卡森-沃克-莱斯科普不变量

The Casson-Walker-Lescop invariant of periodic three-manifolds

Let $p$ be an odd prime and $G$ the finite cyclic group of order $p$. We use the Casson-Walker-Lescop invariant to find a necessary condition for a three-manifold to have an action of $G$ with a circle as the set of fixed points.

Seifert surgery on knots via Reidemeister torsion and Casson-Walker-Lescop invariant

For a knot $K$ with $Δ_K(t)\doteq t^2-3t+1$ in a homology $3$-sphere, let $M$ be the result of $2/q$-surgery on $K$. We show that appropriate assumptions on the Reidemeister torsion and the Casson-Walker-Lescop invariant of the universal abelian covering of $M$ imply $q=\pm 1$, if $M$ is a Seifert fibered space.

Seifert surgery on knots via Reidemeister torsion and Casson-Walker-Lescop invariant II

For a knot $K$ with $Δ_K(t)\doteq t^2-3t+1$ in a homology $3$-sphere, let $M$ be the result of $2/q$-surgery on $K$. We show that an appropriate assumption on the Reidemeister torsion of the universal abelian covering of $M$ implies $q=\pm 1$, if $M$ is a Seifert fibered space.

The Casson-Walker-Lescop Invariant and Link Invariants

Formulas previously presented for the Casson-Walker invariant are generalized to Lescop's extension. These formulas in terms of linking numbers and surgery coefficients compute the change in Lescop's invariant under crossing changes in a framed link presenting a 3-manifold. This leads us to revisit an old formula for a coefficient of the Conway polynomial. Finally we compute Lescop's invariant of several lens spaces and deduce some values for Dedekind sums.

仅 cosmetic 手术与 Casson-Walker-Lescop 不变量

Purely cosmetic surgeries and Casson--Walker--Lescop invariants

该研究证明了在有理同调球面中，无向同调结至多有两个整数纯 cosmetic 手术，并探讨了相关 3-流形中结的同胚性质。

Seifert surgery on knots via Reidemeister torsion and Casson-Walker-Lescop invariant III

For a knot $K$ in a homology $3$-sphere $Σ$, let $M$ be the result of $2/q$-surgery on $K$, and let $X$ be the universal abelian covering of $M$. Our first theorem is that if the first homology of $X$ is finite cyclic and $M$ is a Seifert fibered space with $N\ge 3$ singular fibers, then $N\ge 4$ if and only if the first homology of the universal abelian covering of $X$ is infinite. Our second theorem is that under an appropriate assumption on the Alexander polynomial of $K$, if $M$ is a Seifert fibered space, then $q=\pm 1$ (i.e.\ integral surgery).