拼接的瑞德米斯特扭转像的有限性

Q4 Mathematics Annales Mathematiques Blaise Pascal Pub Date : 2019-04-04 DOI:10.5802/ambp.389

Teruaki Kitano, Yuta Nozaki

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引用次数: 3

摘要

3流形$M$的$\mathit｛SL｝（2，\mathbb｛C｝）$-Reidemeister扭转的值的集合$\mathit{RT｝（M）$既可以是有限的，也可以是无限的。我们证明了$\mathit{RT}（M）$是一个有限集，如果$M$是3-球面中两个特定结的拼接。证明是基于对结的性质变化和$A$-多项式的观察。

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Finiteness of the image of the Reidemeister torsion of a splice

The set $\mathit{RT}(M)$ of values of the $\mathit{SL}(2,\mathbb{C})$-Reidemeister torsion of a 3-manifold $M$ can be both finite and infinite. We prove that $\mathit{RT}(M)$ is a finite set if $M$ is the splice of two certain knots in the 3-sphere. The proof is based on an observation on the character varieties and $A$-polynomials of knots.

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