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PERIODIC VIRTUAL LINKS AND THE BINARY BRACKET POLYNOMIAL

MYEONG-JU JEONG

Department of Mathematics, Korea Science Academy, 111 Baekyang Gwanmun-Ro, Busanjin-Gu, Busan 614-822, Korea

Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea

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and

CHAN-YOUNG PARK

Department of Mathematics, Korea Science Academy, 111 Baekyang Gwanmun-Ro, Busanjin-Gu, Busan 614-822, Korea

Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea

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https://doi.org/10.1142/S0218216511009789Cited by:5 (Source: Crossref)

Abstract

L. H. Kauffman defined the binary bracket polynomial of a virtual link by introducing binary labelings into the states of a virtual link diagram. We use the invariant by a slight modification, and call it the modified b-polynomial. We prove that if a virtual link K has a period p^l for a prime p and a positive integer l, then the modified b-polynomial Inv_K (A) of K is congruent to Inv_K* (A) modulo p and A^{4p^l}-1 where K* is the mirror image of K. We exhibit examples of virtual links whose periods are completely determined by the invariant.

Keywords:

AMSC: 57M25, 57M27

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Journal cover image

Vol. 21, No. 03

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Downloaded 58 times

History

Received 8 September 2008

Accepted 13 January 2011

Published: 20 January 2012

Keywords