The Hanna Neumann conjecture: A flow detection approach

"The Hanna Neumann Conjecture states that if two subgroups of a finitely generated free group have finite ranks m and n, then their intersection has rank N which satisfies $N$ $-$ 1 $\leq$ ($m$ $-$ 1)($n$ $-$ 1). The current work examines this conjecture by restating it in terms of a stronger conjecture on the pullback in a particular category of graphs. The notion of a vertex pairing is developed, and shown to have a direct bearing on the pullback conjecture. In this light, the Flow Conjecture is stated, and its relationship as an apparently stronger conjecture than the Hanna Neumann Conjecture becomes evident. We then prove the Flow Conjecture for certain special cases by detecting a special kind of ""short"" flow. Finally, we examine the properties of projection and non-projection flows that are intended to lead to a full solution to the Hanna Neumann Conjecture."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Feuerman, Kenneth Edward

• Mathematics

Statement dc:rights

• Copyright 1991 Feuerman, Kenneth Edward

Language dc:language

eng

Identifier

AAI9124411
(UMI)AAI9124411

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/20395