Skein modules of links in cylinders over surfaces
We define the Conway skein module 𝒞 (M) of ordered based links in a 3-manifold M. This module gives rise to 𝒞 (M)-valued invariants of usual links in M. We determine a basis of the ℤ[z]-module 𝒞 (Σ×[0,1])/Tor (𝒞 (Σ×[0,1])), where Σ is the real projective plane or a surface with boundary. For cylinde...
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120201181X |
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| _version_ | 1832545818431717376 |
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| author | Jens Lieberum |
| author_facet | Jens Lieberum |
| author_sort | Jens Lieberum |
| collection | DOAJ |
| description | We define the Conway skein module 𝒞 (M) of ordered based links in a 3-manifold M. This module gives rise to 𝒞 (M)-valued invariants of usual links in M. We determine a basis of the ℤ[z]-module 𝒞 (Σ×[0,1])/Tor (𝒞 (Σ×[0,1])), where Σ is the real projective plane or a surface with boundary. For cylinders over the Möbius strip or the projective plane, we derive special properties of the Conway skein module, among them a refinement of a theorem of Hartley and Kawauchi about the Conway polynomial of strongly positive amphicheiral knots in S3. In addition, we determine the Homfly and Kauffman skein modules of Σ×[0,1] where Σ is an oriented surface with boundary. |
| format | Article |
| id | doaj-art-dfdb703225204c11b64a35ef481da85b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-dfdb703225204c11b64a35ef481da85b2025-02-03T07:24:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0132951555410.1155/S016117120201181XSkein modules of links in cylinders over surfacesJens Lieberum0Mathematisches Institut, Universität Basel, Rheinsprung 21, Basel CH-4051, SwitzerlandWe define the Conway skein module 𝒞 (M) of ordered based links in a 3-manifold M. This module gives rise to 𝒞 (M)-valued invariants of usual links in M. We determine a basis of the ℤ[z]-module 𝒞 (Σ×[0,1])/Tor (𝒞 (Σ×[0,1])), where Σ is the real projective plane or a surface with boundary. For cylinders over the Möbius strip or the projective plane, we derive special properties of the Conway skein module, among them a refinement of a theorem of Hartley and Kawauchi about the Conway polynomial of strongly positive amphicheiral knots in S3. In addition, we determine the Homfly and Kauffman skein modules of Σ×[0,1] where Σ is an oriented surface with boundary.http://dx.doi.org/10.1155/S016117120201181X |
| spellingShingle | Jens Lieberum Skein modules of links in cylinders over surfaces International Journal of Mathematics and Mathematical Sciences |
| title | Skein modules of links in cylinders over surfaces |
| title_full | Skein modules of links in cylinders over surfaces |
| title_fullStr | Skein modules of links in cylinders over surfaces |
| title_full_unstemmed | Skein modules of links in cylinders over surfaces |
| title_short | Skein modules of links in cylinders over surfaces |
| title_sort | skein modules of links in cylinders over surfaces |
| url | http://dx.doi.org/10.1155/S016117120201181X |
| work_keys_str_mv | AT jenslieberum skeinmodulesoflinksincylindersoversurfaces |