  With its boundary tracing out a link or knot in 3D, the Seifert surface is a
2D surface of core importance to topological classification. We propose the
first-ever experimentally realistic setup where Seifert surfaces emerge as the
boundary states of 4D topological matter. Unlike ordinary real space knots that
exist in polymers, biomolecules and everyday life, our knots and their Seifert
surfaces exist as momentum space nodal structures, where topological linkages
have profound effects on optical and transport phenomena. Realized with 4D
circuit lattices, our nodal Seifert systems are freed from symmetry constraints
and readily tunable due to the dimension and distance agnostic nature of
circuit connections. Importantly, their Seifert surfaces manifest as very
pronounced impedance peaks in their 3D-imaging via impedance measurements, and
are directly related to knot invariants like the Alexander polynomial and knot
Signature. This work thus unleashes the great potential of Seifert surfaces as
sophisticated yet accessible mathematical tools in the study of exotic band
structures.
