A short exposition of S. Parsa's theorems on intrinsic linking and non-realizability

A. Skopenkov

doi:10.1007/s00454-019-00158-y

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arXiv · 1808.08363

A short exposition of S. Parsa's theorems on intrinsic linking and non-realizability

A. Skopenkov

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Abstract

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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A. Skopenkov. 2020-07-03. A short exposition of S. Parsa's theorems on intrinsic linking and non-realizability. https://doi.org/10.1007/s00454-019-00158-y

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