The Sticky Matroid Conjecture

TL;DR

This paper proves Kantor's conjecture for rank 4, thereby confirming the sticky matroid conjecture and resolving the entire conjecture through a series of logical equivalences and prior results.

Contribution

It establishes the validity of Kantor's conjecture in rank 4, confirming the sticky matroid conjecture and completing the proof of Kantor's conjecture.

Findings

Kantor's conjecture holds in rank 4

The sticky matroid conjecture is proven in this rank

Complete proof of Kantor's conjecture achieved

Abstract

We show Kantor's conjecture (1974) holds in rank 4. This proves both the sticky matroid conjecture of Poljak and Turzik (1982) and the whole Kantor's conjecture, due to an argument of Bachem, Kern, and Bonin, and an equivalence argument of Hochstattler and Wilhelmi, respectively.