On the Embeddability of Skeleta of Spheres

TL;DR

This paper explores the conditions under which the skeleta of spheres can be embedded, extending classical theorems and connecting to the longstanding g-conjecture in combinatorial topology.

Contribution

It generalizes the van Kampen-Flores Theorem and links it to the g-conjecture for simplicial spheres, offering new insights into embeddability problems.

Findings

Extended the van Kampen-Flores Theorem to broader contexts

Established connections between embeddability and the g-conjecture

Provided new criteria for the embeddability of sphere skeleta

Abstract

We consider a generalization of the van Kampen-Flores Theorem and relate it to the long-standing $g$-conjecture for simplicial spheres.