Submultiplicativity and the Hanna Neumann Conjecture

In this article, we dene submultiplicativity of ‘ 2 -numbers in the category of -complexes over a given -complex ^ X, which generalizes the statement of the Strengthened Hanna Neumann Conjecture (SHNC). In the case when is a left-orderable group and ^ X is a free -complex, we prove submultiplicativity for the subcategory consisting of -ordered leafages over ^ X with an additional analytic assumption called the deep-fall property. We show that the deep-fall property is satised for graphs. This implies SHNC.

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