The Hanna Neumann conjecture: A flow detection approach
Feuerman, Kenneth Edward
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https://hdl.handle.net/2142/20395
Description
Title
The Hanna Neumann conjecture: A flow detection approach
Author(s)
Feuerman, Kenneth Edward
Issue Date
1991
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
"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."
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