A result in quantum topology identifying, at roots of unity, the Bonahon-Wong-Yang (BWY) invariants of a pseudo-Anosov surface homeomorphism with the 1-loop invariant of its mapping torus - conjectured in general and proved for once-punctured torus bundles. The identification explains the topological invariance of the BWY invariants and derives their all-orders volume conjecture (with exponentially small corrections) from the quantum modularity conjecture, gives efficient numerical computation of the invariants' perturbative asymptotics, and introduces descendant invariants conjecturally related by a Fourier transform.
This quantum-topology research paper (math.GT) by Garoufalidis and Yu conjectures - and proves for once-punctured torus bundles - that the Bonahon-Wong-Yang (BWY) invariants of pseudo-Anosov homeomor…