  Defective spectral degeneracy, known as exceptional point (EP), lies at the
heart of various intriguing phenomena in optics, acoustics, and other
nonconservative systems. Despite extensive studies in the past two decades, the
\textit{collective} behaviors (e.g., annihilation, coalescence, braiding, etc.)
involving multiple exceptional points or lines and their interplay have been
rarely understood. Here we put forward a universal non-Abelian conservation
rule governing these collective behaviors in generic multiband non-Hermitian
systems and uncover several counterintuitive phenomena. We demonstrate that two
EPs with opposite charges (even the pairwise created) do not necessarily
annihilate, depending on how they approach each other. Furthermore, we unveil
that the conservation rule imposes strict constraints on the permissible
exceptional-line configurations. It excludes structures like Hopf link yet
permits novel staggered rings composed of noncommutative exceptional lines.
These intriguing phenomena are illustrated by concrete models which could be
readily implemented in platforms like coupled acoustic cavities, optical
waveguides, and ring resonators. Our findings lay the cornerstone for a
comprehensive understanding of the exceptional non-Abelian topology and shed
light on the versatile manipulations and applications based on exceptional
degeneracies in nonconservative systems.
