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Polynomial and signature invariants for pseudo-links via Goeritz matrices

Department of Mathematics, Graduate School of Natural Sciences, Pusan National University, Busan 46241, Republic of Korea

E-mail Address: j00399501303@pusan.ac.kr

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Jieon Kim

Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea

E-mail Address: jieonkim7@gmail.com

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, and

Sang Youl Lee

Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea

E-mail Address: sangyoul@pusan.ac.kr

Corresponding author.

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https://doi.org/10.1142/S0218216522500602Cited by:0 (Source: Crossref)

Abstract

In this paper, we introduce the Goeritz matrix for a pseudo-link whose entries lie in the Laurent polynomial ring $ℤ [u^{- 1}, u]$ , which generalizes the Goeritz matrix for a classical link. We show that the determinant of a modified Goeritz matrix gives a Laurent polynomial invariant for pseudo-links in one variable u with integer coefficients. We also introduce the notions of the signature, determinant, and nullity of pseudo-links. Further, we discuss some properties of the invariants and compute the polynomials and those numerical invariants for several pseudo-knot families.

Keywords:

AMSC: 57K10, 57K12, 57K14

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