Essential twisted surfaces in alternating link complements
Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding che...
| Main Authors: | , |
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| Format: | Journal article |
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Mathematical Sciences Publishers
2016
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| _version_ | 1797091541859172352 |
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| author | Lackenby, M Purcell, J |
| author_facet | Lackenby, M Purcell, J |
| author_sort | Lackenby, M |
| collection | OXFORD |
| description | Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface increases in complexity with crossing number. In this paper, we generalize checkerboard surfaces to certain immersed surfaces, called twisted checkerboard surfaces, whose geometry better reflects that of the alternating link in many cases. We describe the surfaces, show that they are essential in the complement of an alternating link, and discuss their properties, including an analysis of homotopy classes of arcs on the surfaces in the link complement. |
| first_indexed | 2024-03-07T03:34:35Z |
| format | Journal article |
| id | oxford-uuid:bbda5e69-f8f3-4540-b34a-59059a2400fe |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:34:35Z |
| publishDate | 2016 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | oxford-uuid:bbda5e69-f8f3-4540-b34a-59059a2400fe2022-03-27T05:20:02ZEssential twisted surfaces in alternating link complementsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bbda5e69-f8f3-4540-b34a-59059a2400feSymplectic Elements at OxfordMathematical Sciences Publishers2016Lackenby, MPurcell, JCheckerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface increases in complexity with crossing number. In this paper, we generalize checkerboard surfaces to certain immersed surfaces, called twisted checkerboard surfaces, whose geometry better reflects that of the alternating link in many cases. We describe the surfaces, show that they are essential in the complement of an alternating link, and discuss their properties, including an analysis of homotopy classes of arcs on the surfaces in the link complement. |
| spellingShingle | Lackenby, M Purcell, J Essential twisted surfaces in alternating link complements |
| title | Essential twisted surfaces in alternating link complements |
| title_full | Essential twisted surfaces in alternating link complements |
| title_fullStr | Essential twisted surfaces in alternating link complements |
| title_full_unstemmed | Essential twisted surfaces in alternating link complements |
| title_short | Essential twisted surfaces in alternating link complements |
| title_sort | essential twisted surfaces in alternating link complements |
| work_keys_str_mv | AT lackenbym essentialtwistedsurfacesinalternatinglinkcomplements AT purcellj essentialtwistedsurfacesinalternatinglinkcomplements |