表面群的Hanna-Neumann猜想

IF 1.3 1区数学 Q1 MATHEMATICS

Compositio Mathematica Pub Date : 2022-09-01 DOI:10.1112/S0010437X22007709

Yago Antolín, A. Jaikin-Zapirain

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引用次数: 13

摘要

汉纳·诺伊曼猜想是关于自由群的两个有限生成子群的交点的秩的表述。这个猜想是由汉娜·诺伊曼在1957年提出的。2011年，乔尔·弗里德曼(Joel Friedman)和伊戈尔·米涅耶夫(Igor Mineyev)独立证明了这一猜想的强化版本。本文证明了强化汉纳·诺伊曼猜想不仅在自由群中成立，而且在不可解表面群中也成立。此外，我们还证明了在自由基团和表面基团中的缩回是惰性的。这意味着自由群和面群的Dicks-Ventura惯性猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Hanna Neumann conjecture for surface groups

The Hanna Neumann conjecture is a statement about the rank of the intersection of two finitely generated subgroups of a free group. The conjecture was posed by Hanna Neumann in 1957. In 2011, a strengthened version of the conjecture was proved independently by Joel Friedman and by Igor Mineyev. In this paper we show that the strengthened Hanna Neumann conjecture holds not only in free groups but also in non-solvable surface groups. In addition, we show that a retract in a free group and in a surface group is inert. This implies the Dicks–Ventura inertia conjecture for free and surface groups.

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来源期刊

Compositio Mathematica 数学-数学

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Compositio Mathematica is a prestigious, well-established journal publishing first-class research papers that traditionally focus on the mainstream of pure mathematics. Compositio Mathematica has a broad scope which includes the fields of algebra, number theory, topology, algebraic and differential geometry and global analysis. Papers on other topics are welcome if they are of broad interest. All contributions are required to meet high standards of quality and originality. The Journal has an international editorial board reflected in the journal content.