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.