A Counterexample to a conjecture of Bosio and Meersseman

TL;DR

This paper presents a counterexample to a conjecture by Bosio and Meersseman, which proposed a specific topological structure for certain complex manifolds associated with dual neighborly polytopes.

Contribution

The paper provides the first known counterexample to the conjecture, challenging the assumed topological equivalence.

Findings

Counterexample disproves the conjecture

Shows the complexity of the topology of Zp

Questions the generality of the conjecture

Abstract

In a paper of Bosio and Meersseman (Real quadrics in Cn, complex manifolds and convex polytopes) the following is conjectured: If P is dual neighborly, then Zp is diffeomorphic to the connected sum of products of spheres. In this paper a counterexample is provided.