English

The quantum G_2 link invariant

Quantum Algebra 2016-09-06 v1 Geometric Topology

Abstract

We derive an inductive, combinatorial definition of a polynomial-valued regular isotopy invariant of links and tangled graphs. We show that the invariant equals the Reshetikhin-Turaev invariant corresponding to the exceptional simple Lie algebra G_2. It is therefore related to G_2 in the same way that the HOMFLY polynomial is related to A_n and the Kauffman polynomial is related to B_n, C_n, and D_n. We give parallel constructions for the other rank 2 Lie algebras and present some combinatorial conjectures motivated by the new inductive definitions.

Keywords

Cite

@article{arxiv.math/9201302,
  title  = {The quantum G_2 link invariant},
  author = {Greg Kuperberg},
  journal= {arXiv preprint arXiv:math/9201302},
  year   = {2016}
}

Comments

Some diagrams at the end are missing