Adiabatic connection of the gapped many-body states is a conceptual background of the topological phases. Historical and more than successful examples are given by various fractional quantum Hall states. Although it is widely used/believed, but not much has been confirmed with sufficient scientific justification, especially with topological degeneracy. The naive expectation of the adiabatic connection does not work due to the abrupt change of the degeneracy of the ground state multiple. What really occurs is an adiabatic connection of the many-body gap. In the recent paper, we have supplied such a justification with spins: “Adiabatic continuity of the spinful quantum Hall states” by Koji Kudo and Yasuhiro Hatsugai, which has been accepted on 28 July 2022 and published in Phys. Rev. B 106, 075120 (2022). See also, arXiv:2201.07893.