Counterintuitive collision of exceptional points on nonorientable manifolds

Band degeneracies, from Hermitian Dirac points to non-Hermitian exceptional points (EPs), are central to topological physics. Beyond individual topology, their interactions yield richer phenomena—such as non-annihilating collisions of pairwise-created point degeneracies, previously thought to occur only in non-Abelian multiband systems. Here, we theoretically and experimentally demonstrate that such nontrivial collisions can arise even in simple two-band Abelian systems, enabled by the nonorientability of momentum-space manifolds. By designing a mixed-dimensional non-Hermitian acoustic lattice, we measure two independent yet complementary topological invariants—band braid and Berry phase—to unambiguously show that two EPs, pairwise created from a hybrid point, merge into a distinct vortex point upon re-encounter, instead of annihilating. Using a path-squeezing criterion, we further confirm the underlying mechanism for such counterintiuitive collision: the braid charge of an EP inverts upon traversing a nonorientable boundary. Our findings identify the geometric nonorientability as a new arena for engineering interactions of band degeneracies, and pave the way for further exploring exceptional topology on nonorientable manifolds. Non-annihilating collisions of band degeneracies were thought to require complex multiband systems. Here, authors demonstrate such collisions in a simple two-band acoustic lattice by leveraging the non-orientable geometry of momentum space, and reveal that the topological charge of an exceptional point reverses upon crossing a non-orientable boundary.