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SIGNATURE, NULLITY AND DETERMINANT OF CHECKERBOARD COLORABLE VIRTUAL LINKS

YOUNG HO IM

Department of Mathematics, Pusan National University, Pusan 609-735, Korea

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KYEONGHUI LEE

Department of Mathematics, Graduate School of Natural Sciences, Pusan National University, Pusan 609-735, Korea

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, and

SANG YOUL LEE

Department of Mathematics, Pusan National University, Pusan 609-735, Korea

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https://doi.org/10.1142/S0218216510008315Cited by:11 (Source: Crossref)

Abstract

In this paper, we present the Goeritz matrix for checkerboard colorable virtual links or, equivalently, checkerboard colorable links in thickened surfaces S_g × [0, 1], which is an extension of the Goeritz matrix for classical knots and links in ℝ³. Using this, we show that the signature, nullity and determinant of classical oriented knots and links extend to those of checkerboard colorable oriented virtual links.

Keywords:

AMSC: 57M25, 57M27

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