Towards the Hanna Neumann conjecture using Dicks' method

• 成果类型: Article
• 署名作者: Tardos, G
• 署名单位: HUN-REN; HUN-REN Institute for Computer Science & Control; Hungarian Academy of Sciences
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/BF01232368
• 发表日期: 1996
• 页码: 95-104
• 关键词: finitely generated subgroups; intersections

摘要

The Hanna Neumann conjecture states that the intersection of two nontrivial subgroups of rank k + 1 and I + 1 of a free group has rank at most kl + 1. In a recent paper [3] W. Dicks proved that a strengthened form of this conjecture is equivalent to his amalgamated graph conjecture. He used this equivalence to reprove all known upper bounds on the rank of the intersection. We use his method to improve these bounds. In particular we prove an upper bound of 2kl - k - l + 1 for the rank of the intersection above (k, I greater than or equal to 2) improving the earlier 2kl - min(k, I) bound of [1]. We prove a special case of the amalgamated graph conjecture in the hope that it may lead to a proof of the general case and thus of the strengthened Hanna Neumann conjecture.