Nonconcordant links with homology cobordant zero-framed surgery manifolds

Cha, J. C. and Powell, M. (2014) Nonconcordant links with homology cobordant zero-framed surgery manifolds. Pacific Journal of Mathematics, 272(1), pp. 1-33. (doi: 10.2140/PJM.2014.272.1)

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We use topological surgery theory to give sufficient conditions for the zero-framed surgery manifold of a 3-component link to be homology cobordant to the zero-framed surgery on the Borromean rings (also known as the 3-torus) via a topological homology cobordism preserving the free homotopy classes of the meridians. This enables us to give examples of 3-component links with unknotted components and vanishing pairwise linking numbers, such that any two of these links have homology cobordant zero-surgeries in the above sense, but the zero-surgery manifolds are not homeomorphic. Moreover, the links are not concordant to one another, and in fact they can be chosen to be height h but not height h + 1 symmetric grope concordant, for each h which is at least three.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Powell, Dr Mark
Authors: Cha, J. C., and Powell, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Pacific Journal of Mathematics
Publisher:Mathematical Sciences Publisher
ISSN (Online):1945-5844
Published Online:09 October 2014
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