On the peripheral subgroups of irreducible 3-manifold groups and acylindrical splittings

2017/05/17 by Filippo Cerocchi, Cerocchi, Filippo · 1 citation
Mathematics · #20E08 #57M05 #57M60 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20E08 #msc:57M05 #msc:57M60

paper · pdf · doi:10.48550/arxiv.1705.06124

23 pages; corrected typos. Added a Proposition in section 4.1 (Proposition 4.5)

arxiv created 2017/10/19 · arxiv updated 2017/10/20

Abstract

We survey the problem of separation under conjugacy and malnormality of the abelian peripheral subgroups of an orientable, irreducible 3-manifold X. We shall focus on the relation between this problem and the existence of acylindrical splittings of π₁(X) as an amalgamated product or HNN-extension along the abelian subgroups corresponding to the JSJ-tori.

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