Knot Concordance and Homology Cobordism

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dc.citation.firstpage2193
dc.citation.issueNumber6
dc.citation.journalTitleProceedings of the American Mathematical Society
dc.citation.lastpage2208
dc.citation.volumeNumber141
dc.contributor.authorCochran, Tim D.
dc.contributor.authorFranklin, Bridget D.
dc.contributor.authorHedden, Matthew
dc.contributor.authorHorn, Peter D.
dc.date.accessioned2013-09-13T16:15:57Z
dc.date.available2013-09-13T16:15:57Z
dc.date.issued2013-06
dc.description.abstractWe consider the question: “If the zero-framed surgeries on two oriented knots in S3 are Z-homology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?” We show that this question has a negative answer in the smooth category, even for topologically slice knots. To show this we first prove that the zero-framed surgery on K is Z-homology cobordant to the zero-framed surgery on many of its winding number one satellites P(K). Then we prove that in many cases the τ and s-invariants of K and P(K) differ. Consequently neither τ nor s is an invariant of the smooth homology cobordism class of the zero-framed surgery. We also show that a natural rational version of this question has a negative answer in both the topological and smooth categories by proving similar results for K and its (p, 1)-cables.
dc.embargo.termsnone
dc.identifier.citationCochran, Tim D., Franklin, Bridget D., Hedden, Matthew, et al.. "Knot Concordance and Homology Cobordism." <i>Proceedings of the American Mathematical Society,</i> 141, no. 6 (2013) American Mathematical Society: 2193-2208. http://dx.doi.org/10.1090/S0002-9939-2013-11471-1.
dc.identifier.doihttp://dx.doi.org/10.1090/S0002-9939-2013-11471-1
dc.identifier.urihttps://hdl.handle.net/1911/71900
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.titleKnot Concordance and Homology Cobordism
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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