The multi-variable Affine Index Polynomial for tangles

2022/07/25 by Petit, Nicolas
#57K12 #57K14 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2207.12300

Abstract

The multi-variable affine index polynomial was defined by the author in previous work. The aim of this short note is to update the definition so it is generalizable to virtual tangles and to show it is compatible with tangle decomposition. We also introduce the Turaev moves for virtual tangles, and discuss how to recover the weight of each crossing as an intersection pairing of homology classes.

Related

• The Multi-variable Affine Index Polynomial
• A Linking Number Definition of the Affine Index Polynomial and Applications
• The Affine Index Polynomial and the Sawollek Polynomial
• Invariants of virtual links and twisted links using affine indices
• The Wriggle polynomial for virtual tangles