We present a short statement and proof of the following result by S. Parsa. Let L be a graph such that the join L*\{1,2,3\} (i.e. the union of three cones over L along their common bases) piecewise linearly (PL) embeds into \mathbb R^4. Then L admits 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 .
We present a short exposition of the following results by S. Parsa. Let L be a graph such that the join L*\{1,2,3\} (i.e. the union of three cones over L along their common bases) piecewise linearly (PL) embeds into \mathbb R^4. Then L admits a PL embedding into \mathbb R^3 such that any two disjoint cycles have zero linking number. There is C such that every 2-dimensional simplicial complex having n vertices and embeddable into \mathbb R^4 contains less than Cn^{5/3 .
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We also clarify its relation to earlier publications
There is C such that every 2-dimensional simplicial complex having n vertices and embeddable into \mathbb R^4 contains less than Cn^{5/3