Groups, Graphs, and the Hanna Neumann Conjecture

Abstract

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.

Extracted Key Phrases

Showing 1-7 of 7 references

Ann. of Math

  • Submultiplicativity, Hanna Neumann, Conjecture
  • 2012
2 Excerpts

On the intersection of finitely generated free groups

  • H Neumann
  • 1956
1 Excerpt

On the free product of ordered groups

  • A A Vinogradov
  • 1949

On the theory of partially ordered groups

  • H Shimbireva
  • 1947