# Submultiplicativity and the Hanna Neumann Conjecture | Annals of Mathematics

Abstract In this article, we define submultiplicativity of ℓ2-numbers in the category of Γ-complexes over a given Γ-complex X^, which generalizes the statement of the Strengthened Hanna Neumann Conjecture (SHNC). In the case when Γ is a left-orderable group and X^ is a free Γ-complex, we prove submultiplicativity for the subcategory consisting of Γ-ordered leafages over X^ with an additional analytic assumption called the deep-fall property. We show that the deep-fall property is satisfied for graphs. This implies SHNC.

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### 数学年刊（Annals of Mathematics）

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