Liftings of knots in S_g × S¹ and covering of virtual knots

2023/09/18 by Seongjeong Kim, Kim, Seongjeong
Mathematics · #57K10 #57K12 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2309.09583

openalex publication_date 2023/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A virtual link diagram is called \em (mod m) almost classical if it admits a (mod m) Alexander numbering. In \citeBodenGaudreauHarperNicasWhite, it is shown that Alexander polynomial for almost classical links can be defined by using the homology of the associated infinite cyclic cover. On the other hand, in \citeNaokoKamada an infinite family of m fold covering over a virtual knot is constructed so that it is mod m almost classical link for all m by using oriented cut point. In this paper, another way to obtain a family of m-fold coverings over a given virtual knots, which are mod m almost classical, by using knots in S_g × S¹.

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