Two aspects of graph 3-manifold groups

Abstract

We prove that fundamental groups of graph 3-manifolds are virtually poly-free and lie in the family Lex. As a consequence, we prove that all finitely generated 3-manifold groups also have these two properties. The first property is a purely group-theoretical concept, and the second is related to the left-exactness property of bounded cohomology of groups. Both properties are proved by constructing sequences of covers of graph 3-manifolds.

Disclosure

“ns (Proposition 6.1). Theorem 1.4 and Corollary 1.5 will be proved in Sections 7 and 8, respectively. Role of AI. The proof of the second half of Lemma 7.2 was generated by Google Gemini, and checked by the author. The author also used Google Gemini to search for references and to translate [Bra, Bou]. Acknowledgment. The author thanks Xiaolei Wu for asking him whether graph 3-manifold groups are virtually poly-free. The author thanks Lvzhou Chen for asking him whether graph 3-mani”

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2026-08-24T00:34:05.733Z

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