Abstract
Let M be a closed, orientable, irreducible, geometrizable 3-manifold. We prove that the profinite topology on the fundamental group of π 1(M) is efficient with respect to the JSJ decomposition of M. We go on to prove that π 1(M) is good, in the sense of Serre, if all the pieces of the JSJ decomposition are. We also prove that if M is a graph manifold then π 1(M) is conjugacy separable.
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Wilton, H., Zalesskii, P. Profinite properties of graph manifolds. Geom Dedicata 147, 29–45 (2010). https://doi.org/10.1007/s10711-009-9437-3
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DOI: https://doi.org/10.1007/s10711-009-9437-3