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 Title: The Hanna Neumann conjecture: A flow detection approach Author(s): Feuerman, Kenneth Edward Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics 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. Issue Date: 1991 Type: Text Language: English URI: http://hdl.handle.net/2142/20395 Rights Information: Copyright 1991 Feuerman, Kenneth Edward Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9124411 OCLC Identifier: (UMI)AAI9124411
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