Graph manifolds have virtually positive Seifert volume

Abstract

This paper shows that the Seifert volume of each closed non-trivial graph manifold is virtually positive. As a consequence, for each closed orientable prime 3-manifold $N$, the set of mapping degrees $cD(M,N)$ 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.

References in corpus (2)

• Non-zero degree maps between $2n$-manifolds
• Non-zero degree maps between 3-manifolds

Cited by in corpus (5)

• Chern--Simons theory, surface separability, and volumes of 3-manifolds
• Positive simplicial volume implies virtually positive Seifert volume for $3$-manifolds
• Volume of representations and mapping degree
• Endomorphisms of mapping tori
• Chern Simons Theory and the volume of 3-manifolds