Homology cobordism and Seifert fibered 3-manifolds
Author
Cochran, Tim D.
Tanner, Daniel
Date
2014Citation
Published Version
Abstract
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 in their first homology. Then we exhibit families of examples of 3-manifolds (obtained by surgery on links), with fixed linking form and cohomology ring, that are not homology cobordant to any Seifert fibered space (as shown by their rational cohomology rings). These examples are shown to represent distinct homology cobordism classes using higher Massey products and Milnor's µ-invariants for links.
Type
Journal article
Citable link to this page
http://hdl.handle.net/1911/94828Metadata
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