Groups, graphs, and the Hanna Neumann conjecture

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Submultiplicativity, an analytic property generalizing the Strengthened Hanna Neumann Conjecture (SHNC) to complexes was proved in [2] assuming the deep-fall property. This in particular implied SHNC. The purpose of this note is to write the proof of the original SHNC and purely in terms of groups and graphs. We also give explicit examples showing that the upper bound in SHNC is sharp.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalJournal of Topology and Analysis
Issue number1
StatePublished - Mar 2012


  • Group
  • Hanna Neumann Conjecture
  • deep-fall property
  • essential set
  • fall
  • flower
  • forest
  • garden
  • graph
  • ladder
  • leaf
  • leafage
  • left-orderable
  • order-essential edge
  • system of graphs
  • tree
  • vein

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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