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SUMMARY:Two-generator subgroups of free-by-cyclic groups - Edgar Bering (S
 JSU)
DTSTART:20241122T134500Z
DTEND:20241122T144500Z
UID:TALK220843@talks.cam.ac.uk
CONTACT:Francesco Fournier-Facio
DESCRIPTION:In general\, the classification of finitely generated subgroup
 s of a given group is intractable. Restricting to two-generator subgroups 
 in a geometric setting is an exception. For example\, a two-generator subg
 roup of a right-angled Artin group is either free or free abelian. Jaco an
 d Shalen proved that a two-generator subgroup of the fundamental group of 
 an orientable atoroidal irreducible 3-manifold is either free\, free-abeli
 an\, or finite-index. In this talk I will present recent work proving a si
 milar classification theorem for two generator mapping-torus groups of fre
 e group endomorphisms: every two generator subgroup is either free or conj
 ugate to a sub-mapping-torus group. As an application we obtain an analog 
 of the Jaco-Shalen result for free-by-cyclic groups with fully irreducible
  atoroidal monodromy. While the statement is algebraic\, the proof techniq
 ue uses the topology of finite graphs\, a la Stallings. This is joint work
  with Naomi Andrew\, Ilya Kapovich\, and Stefano Vidussi.
LOCATION:MR13
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