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} simplices of dimension 2. We also present corrected statement and proof of the analogue of the second result for intrinsic linking.
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^{ 8 /3} simplices of dimension 2. We also present the analogue of the second result for intrinsic linking.
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corrected statement and proof of