On van Kampen-Flores, Conway-Gordon-Sachs and Radon theorems

Abstract

We exhibit relations between van Kampen-Flores, Conway-Gordon-Sachs and Radon theorems, by presenting direct proofs of some implications between them. The key idea is an interesting relation between the van Kampen and the Conway-Gordon-Sachs numbers for restrictions of a map of $(d+2)$-simplex to ${\mathbb{R}}^d$ to the $(d+1)$-face and to the $[d/2]$-skeleton.

The paper is subsumed by the submitted replacement of arXiv:1605.05141

References in corpus (3)

• Combinatorics of embeddings
• Alternative proofs of the Conway-Gordon-Sachs Theorems
• Algebraic proofs of linear versions of the Conway--Gordon--Sachs theorem and the van Kampen--Flores theorem

Cited by in corpus (3)

• Eliminating higher-multiplicity intersections in the metastable dimension range
• A short proof of the Patak-Tancer theorem on non-embeddability of $k$-complexes in $2k$-manifolds
• A `converse' to the Constraint Lemma