Title:
Graph manifolds have virtually positive Seifert volume

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Shicheng Wang

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abstract:
There are two invariants of 3-manifolds which respect maps:
simplicial volume and Seifert volume.
For prime 3-manifolds, simplicial volume detects
exactly their hyperbolic parts
and  3-manifolds with  zero simplicial volume are exactly graph manifolds.

It is proved recently that each closed non-trivial graph manifold has a
finite cover of positive Seifert volume. As a consequence for each closed
orientable prime 3-manifold  N, the set of mapping degrees D(M,N) is
finite for any 3-manifold M unless N is finitely covered by either a torus
bundle, or a trivial circle bundle, or the 3-sphere.

This is joint work with Pierre Derbez.