F_n 的不可约非满自同态是双曲的
群论
2021-10-01 v3
摘要
此前，Reynolds 证明了任何不可约非满自同态都可以由一个有限图上的不可约浸入表示。我们给出了一个新的证明，并且还证明了当浸入具有无割点的连通 Whitehead 图时，其部分逆命题也成立。下一个结果是对自由群中在不可约非满自同态下不变的有限生成子群的一个刻画。因此，不可约非满自同态是完全不可约的。该刻画与 Reynolds 定理共同表明，不可约非满自同态的映射环面是字双曲的。
引用
@article{arxiv.1908.08214,
title = {Irreducible Nonsurjective Endomorphisms of $F_n$ are Hyperbolic},
author = {Jean Pierre Mutanguha},
journal= {arXiv preprint arXiv:1908.08214},
year = {2021}
}
备注
v1: 19 pages, 1 figure. v2: 20 pages, 1 figure. Theorem 4.5 (now 4.6) as previously stated has a counterexample (Example 4.7). We added an extra hypothesis in the statement and adapted the proof accordingly. Consequently, we had to remove the algorithm described at the end of Section 4. Finally, Corollary 4.6 is now Corollary 5.6. v3: Fixed broken references