Bailey Pairs for the Tetrahedron Index

TL;DR

This paper introduces new Bailey pairs related to the tetrahedron index, which is connected to topological invariants of 3-manifolds and knots, potentially enabling novel methods for deriving knot invariants.

Contribution

The authors develop new Bailey pairs for the tetrahedron index's pentagon identity, providing a fresh framework for knot invariant derivation via Bailey chains.

Findings

New Bailey pairs for the tetrahedron index are constructed.

Potential application to deriving knot invariants.

Framework may simplify calculations of 3-manifold invariants.

Abstract

In this work, we develop new Bailey pairs for the pentagon identity satisfied by the tetrahedron index, expressible in terms of $q$-series. Since the tetrahedron index underlies topological invariants of 3-manifolds and related knots, our construction may offer a new framework to deriving knot invariants through the Bailey chain.