Topological phases of matter connect mathematical principles to real materials, and may shape future electronic and quantum technologies. So far, this discipline has mostly focused on single-gap topology described by topological invariants such as Chern numbers. Here, based on a tunable kagome model, we observe non-Abelian band topology and its transitions in acoustic semimetals, in which the multi-gap Hilbert space plays a key role. In non-Abelian semimetals, the topological charges of band nodes are converted through the braiding of nodes in adjacent gaps, and their behaviour cannot be captured by conventional topological band theory. Using kagome acoustic metamaterials and pump–probe measurements, we demonstrate the emergence of non-Abelian topological nodes, identify their dispersions and observe the induced multi-gap topological edge states. By controlling the geometry of the metamaterials, topological transitions are induced by the creation, annihilation, merging and splitting of band nodes. This reveals the underlying rules for the conversion and transfer of non-Abelian topological charges in multiple bandgaps. The resulting laws that govern the evolution of band nodes in non-Abelian multi-gap systems should inspire studies on multi-band topological semimetals and multi-gap topological out-of-equilibrium systems.

物质的拓扑相将数学原理与真实材料联系起来，并可能塑造未来的电子和量子技术。到目前为止，该学科主要关注由拓扑不变量（例如陈数）描述的单间隙拓扑。在这里，基于可调谐的kagome模型，我们观察了非阿贝尔能带拓扑及其在声学半金属中的跃迁，其中多间隙希尔伯特空间起着关键作用。在非阿贝尔半金属中，能带节点的拓扑电荷是通过相邻间隙中节点的编织来转换的，传统的拓扑能带理论无法捕捉到它们的行为。使用 kagome 声学超材料和泵浦探针测量，我们证明了非阿贝尔拓扑节点的出现，识别它们的分散并观察诱导的多间隙拓扑边缘状态。通过控制超材料的几何形状，拓扑跃迁是由能带节点的创建、湮灭、合并和分裂引起的。这揭示了非阿贝尔拓扑电荷在多个带隙中转换和转移的基本规则。由此产生的支配非阿贝尔多能隙系统中能带节点演化的定律应该会激发对多能带拓扑半金属和多能隙拓扑失衡系统的研究。