Sufficient Conditions for Amalgamated 3-Manifolds to be ∂-Irreducible

Abstract

In this paper, the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets of the curve complex and the arc complex of F.

Keywords

∂-Irreducibility / Irreducibility / Amalgamated 3-manifold / Curve complex / Arc complex

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