Title

Oriented Local Moves and Divisibility of the Jones Polynomial

Authors

Paul Drube, Valparaiso University
Puttipong Pongtanapaisan, University of Iowa

Document Type

Article

Publication Date

2019

Abstract

For any virtual link L = S ∪ T that may be decomposed into a pair of oriented n-tangles S and T, an oriented local move of type T 7→ T ′ is a replacement of T with the n-tangle T ′ in a way that preserves the orientation of L. After developing a general decomposition for the Jones polynomial of the virtual link L = S ∪ T in terms of various (modified) closures of T, we analyze the Jones polynomials of virtual links L1, L2 that differ via a local move of type T 7→ T ′ . Succinct divisibility conditions on V (L1) − V (L2) are derived for broad classes of local moves that include the ∆-move and the double-∆-move as special cases. As a consequence of our divisibility result for the double-∆-move, we introduce a necessary condition for any pair of classical knots to be S-equivalent.

Recommended Citation

Drube, Paul and Pongtanapaisan, Puttipong, "Oriented Local Moves and Divisibility of the Jones Polynomial" (2019). Mathematics and Statistics Faculty Publications. 63.
https://scholar.valpo.edu/math_stat_fac_pubs/63