Abstract
We prove that the property of a free group endomorphism being irreducible is a group invariant of the ascending HNN extension it defines. This answers a question posed by Dowdall–Kapovich–Leininger. We further prove that being irreducible and atoroidal is a commensurability invariant. The invariance follows from an algebraic characterization of ascending HNN extensions that determines exactly when their defining endomorphisms are irreducible and atoroidal; specifically, we show that the endomorphism is irreducible and atoroidal if and only if the ascending HNN extension has no infinite index subgroups that are ascending HNN extensions.
Original language | English (US) |
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Pages (from-to) | 47-63 |
Number of pages | 17 |
Journal | Commentarii Mathematici Helvetici |
Volume | 96 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2021 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Atoroidal
- Group invariant
- Irreducible
- Mapping torus