论文标题
Reidemeister Torsion的代数属性
An algebraic property of Reidemeister torsion
论文作者
论文摘要
对于3个manifold $ m $和一个循环$ \ mathit {sl}（2，\ mathbb {c}）$ - 表示其基本组的$ \ mathit {sl {sl}（2，2，\ mathbb {c}）定义。如果只有许多不可约合表示的共轭类别有限，则已知reidemester扭转是代数数。此外，我们证明，对于大多数Seifert光纤空间和无限的许多双曲线3个manifolds，Reidemister扭转不仅是代数数字，而且是代数整数。另外，对于打结外部$ e（k）$，当固定$ρ$限制$ρ$时，我们讨论了$τ_ρ（e（k））$的行为。
For a 3-manifold $M$ and an acyclic $\mathit{SL}(2,\mathbb{C})$-representation $ρ$ of its fundamental group, the $\mathit{SL}(2,\mathbb{C})$-Reidemeister torsion $τ_ρ(M) \in \mathbb{C}^\times$ is defined. If there are only finitely many conjugacy classes of irreducible representations, then the Reidemeister torsions are known to be algebraic numbers. Furthermore, we prove that the Reidemeister torsions are not only algebraic numbers but also algebraic integers for most Seifert fibered spaces and infinitely many hyperbolic 3-manifolds. Also, for a knot exterior $E(K)$, we discuss the behavior of $τ_ρ(E(K))$ when the restriction of $ρ$ to the boundary torus is fixed.
