Nonconcordant links with homology cobordant zero-framed surgery manifolds

Cha, Jae Choon; Powell, Mark

doi:10.2140/pjm.2014.272.1

Nonconcordant links with homology cobordant zero-framed surgery manifolds

Cha, Jae Choon; Powell, Mark

Authors

Jae Choon Cha

Mark Powell

Abstract

We use topological surgery in dimension four to give sufficient conditions for the zero framed surgery manifold of a 3-component link to be homology cobordant to the 3-torus, which arises from zero framed surgery on the Borromean rings, via a topological homology cobordism preserving the homotopy classes of the meridians. This enables us to give new 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 n but not height n+1 symmetric grope concordant, for each n which is at least three.

Citation

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

Journal Article Type	Article
Acceptance Date	Dec 16, 2013
Online Publication Date	Oct 9, 2014
Publication Date	Oct 9, 2014
Deposit Date	Oct 3, 2017
Publicly Available Date	Oct 4, 2017
Journal	Pacific Journal of Mathematics
Publisher	Mathematical Sciences Publishers (MSP)
Peer Reviewed	Peer Reviewed
Volume	272
Issue	1
Pages	1-33
DOI	https://doi.org/10.2140/pjm.2014.272.1
Related Public URLs	https://arxiv.org/abs/1309.5051

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Copyright Statement
First published in Pacific Journal of Mathematics in Vol. 272 (2014), No. 1, 1–33, published by Mathematical Sciences Publishers. © 2014 Mathematical Sciences Publishers. All rights reserved.