论棋盘式可着色虚拟结的行列式

arXiv - MATH - Geometric Topology Pub Date : 2024-08-04 DOI:arxiv-2408.01891

Tomoaki Hatano, Yuta Nozaki

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引用次数: 0

摘要

众所周知，古典结的行列式 mod $8$ 是由 Arf 不变量分类的。博登和卡里米引入了棋盘式可着色虚拟结的行列式。我们证明了它们的行列式 mod $8$ 是由上升多项式中 $z^2$ 的系数分类的，而上升多项式是经典结的康威多项式的扩展。

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On determinant of checkerboard colorable virtual knots

For classical knots, it is well known that their determinants mod $8$ are classified by the Arf invariant. Boden and Karimi introduced a determinant of checkerboard colorable virtual knots. We prove that their determinant mod $8$ is classified by the coefficient of $z^2$ in the ascending polynomial which is an extension of the Conway polynomial for classical knots.

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arXiv - MATH - Geometric Topology

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