Ascending chains of free groups in 3-manifold groups

Autor:	Bering IV, Edgar A., Lazarovich, Nir
Rok vydání:	2021
Předmět:	Mathematics - Group Theory Mathematics - Geometric Topology 57M05 20E07 57K20 57K32
Druh dokumentu:	Working Paper
Popis:	Takahasi and Higman independently proved that any ascending chain of subgroups of constant rank in a free group must stabilize. Kapovich and Myasnikov gave a proof of this fact in the language of graphs and Stallings folds. Using profinite techniques, Shusterman extended this ascending chain condition to limit groups, which include closed surface groups. Motivated by Kapovich and Myasnikov's proof we provide two new proofs of this ascending chain condition for closed surface groups, and establish the ascending chain condition for free subgroups of constant rank in a closed (or finite-volume hyperbolic) 3-manifold group. Hyperbolic geometry, geometrization, and graphs-of-groups decompositions all play a role in our proofs. Comment: 10 pages; v2 adds references to work of Higman and more contrasting non-examples to the introduction
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.11777 Zobrazit plný text záznamu View this record from Arxiv