Submultiplicativity and the Hanna Neumann Conjecture

  title={Submultiplicativity and the Hanna Neumann Conjecture},
  author={Igor Mineyev},
We define submultiplicativity of `-numbers in the category of Γ-complexes over a given Γ-complex X̂, which generalizes the statement of the Strengthened Hanna Neumann Conjecture (SHNC). In the case when Γ is a left-orderable group and X̂ is a free Γ-complex, we prove submultiplicativity for the subcategory consisting of Γ-ordered leafages over X̂ with an additional analytic assumption called the deep-fall property. We show that the deep-fall property is satisfied for graphs. This implies SHNC… CONTINUE READING