2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58999The vanishing of Van Kampen's obstruction is known to be necessary and sufficient for embeddability of a simplicial n-complex into $R^{2n}$ for $n\neq 2$, and it was recently shown to be incomplete for $n=2$. We use algebraic-topological invariants of four-manifolds with boundary to introduce a sequence of higher embedding obstructions for a class of 2-complexes in $R^4$.10 pages; To appear in Proc. Amer. Math. SocGeometric TopologyAlgebraic Topology57M20text