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    Homology cobordism and Seifert fibered 3-manifolds

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    Author
    Cochran, Tim D.
    Tanner, Daniel
    Date
    2014
    Citation
    Cochran, Tim D. and Tanner, Daniel. "Homology cobordism and Seifert fibered 3-manifolds." Proceedings of the American Mathematical Society, 142, (2014) 4015-4024. https://doi.org/10.1090/S0002-9939-2014-12122-8ᅠ.
    Published Version
    https://doi.org/10.1090/S0002-9939-2014-12122-8ᅠ
    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/1911/94828
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    • Faculty Publications [3507]
    • Mathematics Faculty Publications [39]

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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892