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Homology cobordism and Seifert fibered $3$-manifolds
It is known that every closed oriented $3$-manifold is homology cobordant to a hyperbolic $3$-manifold. By contrast we show that many homology cobordism classes contain no Seifert fibered $3$-manifold. This is accomplished by determining the isomorphism type of the rational cohomology ring of all Seifert fibered $3$-manifolds with no $2$-torsion …