Skein modules of links in cylinders over surfaces

Jens Lieberum

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 32, 1-40

Abstract:

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 S 3 . In addition, we determine the Homfly and Kauffman skein modules of Σ × [ 0 , 1 ] where Σ is an oriented surface with boundary.

Date: 2002
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/32/579210.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/32/579210.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:579210

DOI: 10.1155/S016117120201181X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().