NONCONCORDANT LINKS WITH HOMOLOGY COBORDANT ZERO-FRAMED SURGERY MANIFOLDS
SCIE
SCOPUS
- Title
- NONCONCORDANT LINKS WITH HOMOLOGY COBORDANT ZERO-FRAMED SURGERY MANIFOLDS
- Authors
- Cha, JC; Mark Powell
- Date Issued
- 2014-11
- Publisher
- PACIFIC JOURNAL MATHEMATICS
- Abstract
- 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.
- Keywords
- homology cobordism; zero-framed surgery; topological surgery; link concordance; symmetric grope concordance; KNOT CONCORDANCE GROUP; CODIMENSION 2; SLICE-KNOTS; INVARIANTS; L-2-SIGNATURES; 3-MANIFOLDS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/13652
- DOI
- 10.2140/PJM.2014.272.1
- ISSN
- 0030-8730
- Article Type
- Article
- Citation
- PACIFIC JOURNAL OF MATHEMATICS, vol. 272, no. 1, page. 1 - 33, 2014-11
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