A Short Exposition of Salman Parsa’s Theorems on Intrinsic Linking and Non-realizability

We present a short exposition of the following result by Salman Parsa: LetLbe a graph such that the join$$L*\{1,2,3\}$$ (i.e., the union of three cones overLalong their common bases) piecewise linearly (PL) embeds into$$\mathbb {R}^4$$. ThenLadmits a PL embedding into$$\mathbb {R}^3$$such that any two disjoint cycles have zero linking number. We also clarify its relation to earlier publications.