Submultiplicativity and the Hanna Neumann conjecture

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Abstract

In this article, we dene submultiplicativity of ℓ2-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 X is a free Γ-complex, we prove submulti-plicativity 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 satised for graphs. This implies SHNC.

Original languageEnglish (US)
Pages (from-to)393-414
Number of pages22
JournalAnnals of Mathematics
Volume175
Issue number1
DOIs
StatePublished - Jan 2012

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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