Characterization of the reduced peripheral system of links
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866915024877912064 |
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| author | Audoux, Benjamin Meilhan, Jean-Baptiste |
| author_facet | Audoux, Benjamin Meilhan, Jean-Baptiste |
| contents | The reduced peripheral system was introduced by Milnor in the fifties for the study of links up to link-homotopy, i.e. up to isotopies and crossing changes within each link component. However, for four or more components, this invariant does not yield a complete link-homotopy invariant. This paper provides two characterizations of links having the same reduced peripheral system: a diagrammatical one, in terms of link diagrams, seen as welded diagrams up to self-virtualization, and a topological one, in terms of ribbon solid tori in 4--space up to ribbon link-homotopy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1904_04763 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Characterization of the reduced peripheral system of links Audoux, Benjamin Meilhan, Jean-Baptiste Geometric Topology 57M27 (Primary) The reduced peripheral system was introduced by Milnor in the fifties for the study of links up to link-homotopy, i.e. up to isotopies and crossing changes within each link component. However, for four or more components, this invariant does not yield a complete link-homotopy invariant. This paper provides two characterizations of links having the same reduced peripheral system: a diagrammatical one, in terms of link diagrams, seen as welded diagrams up to self-virtualization, and a topological one, in terms of ribbon solid tori in 4--space up to ribbon link-homotopy. |
| title | Characterization of the reduced peripheral system of links |
| topic | Geometric Topology 57M27 (Primary) |
| url | https://arxiv.org/abs/1904.04763 |