Knot Concordance and Homology Cobordism
| dc.citation.firstpage | 2193 | en_US |
| dc.citation.issueNumber | 6 | en_US |
| dc.citation.journalTitle | Proceedings of the American Mathematical Society | en_US |
| dc.citation.lastpage | 2208 | en_US |
| dc.citation.volumeNumber | 141 | en_US |
| dc.contributor.author | Cochran, Tim D. | en_US |
| dc.contributor.author | Franklin, Bridget D. | en_US |
| dc.contributor.author | Hedden, Matthew | en_US |
| dc.contributor.author | Horn, Peter D. | en_US |
| dc.date.accessioned | 2013-09-13T16:15:57Z | en_US |
| dc.date.available | 2013-09-13T16:15:57Z | en_US |
| dc.date.issued | 2013-06 | en_US |
| dc.description.abstract | We 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. | en_US |
| dc.embargo.terms | none | en_US |
| dc.identifier.citation | Cochran, 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. | en_US |
| dc.identifier.doi | http://dx.doi.org/10.1090/S0002-9939-2013-11471-1 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/71900 | en_US |
| dc.language.iso | eng | en_US |
| dc.publisher | American Mathematical Society | en_US |
| dc.rights | Article 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. | en_US |
| dc.title | Knot Concordance and Homology Cobordism | en_US |
| dc.type | Journal article | en_US |
| dc.type.dcmi | Text | en_US |
| dc.type.publication | publisher version | en_US |