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It is known that every closed oriented 3-manifold is homology cobordant to ahyperbolic 3-manifold. By contrast we show that many homology cobordism classescontain no Seifert fibered 3-manifold. This is accomplished by determining theisomorphism type of the rational cohomology ring of all Seifert fibered3-manifolds with no 2-torsion in their first homology. Then we exhibit familiesof examples of 3-manifolds (obtained by surgery on links), with fixed linkingform and cohomology ring, that are not homology cobordant to any Seifertfibered space (as shown by their rational cohomology ring). These examples areshown to represent distinct homology cobordism classes using higher Masseyproducts and Milnor's u-invariants for links.

Homology cobordism and Seifert fibered 3-manifolds