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

Abstract

We present a short exposition of the following results by S. Parsa. Let $L$ be a graph such that the join $L\ast \{1,2,3\}$ (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 $C{n}^{8/3}$ simplices of dimension 2. We also present the analogue of the second result for intrinsic linking.

5 pages; criticism covered by published correction removed

References in corpus (1)

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

Cited by in corpus (2)

• On embeddability of joins and their `factors'
• A short exposition of S. Parsa's theorems on intrinsic linking and non-realizability