Bismut and Lott constructed analytic torsion forms, which extends the Ray-Singer analytic torsion. It remains an open question whether analytic torsion forms satisfy Igusa's axiomatization for higher torsion invariants.
In this talk, I state a gluing formula for analytic torsion forms, which leads to a positive answer to the question. This is a joint work with Martin Puchol and Jialin Zhu. The proof is based on adiabatic limit and Witten deformation.