Submultiplicativity and the Hanna Neumann Conjecture

• 成果类型: Article
• 署名作者: Mineyev, Igor
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.175.1.11
• 发表日期: 2012
• 页码: 393-414
• 关键词: finitely generated subgroups; free-products; intersection; TOPOLOGY

摘要

In this article, we define submultiplicativity of l(2)-numbers in the category of F-complexes over a given F-complex X, which generalizes the statement of the Strengthened Hanna Neumann Conjecture (SHNC). In the case when F is a left-orderable group and X is a free F-complex, we prove submultiplicativity for the subcategory consisting of F-ordered leafages over X with an additional analytic assumption called the deep-fall property. We show that the deep-fall property is satisfied for graphs. This implies SHNC.