  We report on the occurrence of knotted metallic band structures as stable
topological phases in non-Hermitian (NH) systems. These knotted NH metals are
characterized by open Fermi surfaces, known in mathematics as Seifert surfaces,
that are bounded by knotted lines of exceptional points. Quite remarkably, and
in contrast to the situation in Hermitian systems, no fine tuning or symmetries
are required in order to stabilize these exotic phases of matter. By explicit
construction, we derive microscopic tight-binding models hosting knotted NH
metals with strictly short-ranged hopping, and investigate the stability of
their topological properties against perturbations. Building up on recently
developed experimental techniques for the realization of NH band structures, we
discuss how the proposed models may be experimentally implemented in photonic
systems.
