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The multi-variable Affine Index Polynomial for tangles

Geometric Topology 2022-07-26 v1

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.

Keywords

Cite

@article{arxiv.2207.12300,
  title  = {The multi-variable Affine Index Polynomial for tangles},
  author = {Nicolas Petit},
  journal= {arXiv preprint arXiv:2207.12300},
  year   = {2022}
}

Comments

18 pages, 21 figures. Comments welcome!

R2 v1 2026-06-25T01:12:38.641Z