No Access

KAUFFMAN BRACKET SKEIN MODULE OF A FAMILY OF PRISM MANIFOLDS

MACIEJ MROCZKOWSKI

Institute of Mathematics, University of Gdansk, Ul. Wita Stwosza 57, 80-952 Gdansk-Oliwa, Poland

https://doi.org/10.1142/S0218216511008681Cited by:14 (Source: Crossref)

Abstract

Diagrams and Reidemeister moves for links in orientable Seifert manifolds are introduced. Using these diagrams, we compute the Kauffman bracket skein modules of prism manifolds with first homology of order 4. In particular, we show that these modules are free.

Keywords:

AMSC: 57M27

References

P. Gilmer and J. Harris, J. Knot Theory Ramifications 16, 103 (2007). Link, Web of Science, Google Scholar
J. Hoste and J. H. Przytycki, Math. Z. 220(1), 63 (1995), DOI: 10.1007/BF02572603. Google Scholar
J. Hoste and J. H. Przytycki, J. Knot Theory Ramifications 2(3), 321 (1993). Link, Google Scholar
M. Mroczkowski and M. Dabkowski, Topol. Appl. 156, 1831 (2009), DOI: 10.1016/j.topol.2009.03.045. Crossref, Web of Science, Google Scholar
M. Mroczkowski, Kauffman bracket skein module of the connected sum of two projective spaces, to appear in J. Knot Theory Ramifications , arXiv:1008.1007 . Google Scholar
P. Orlik , Seifert Manifolds , Lecture Notes in Mathematics 291 ( Springer , 1972 ) . Crossref, Google Scholar
J. H. Przytycki, Bull. Polish Acad. Sci. 39(2), 91 (1991). Google Scholar
V. G. Turaev, J. Soviet Math. 52, 2799 (1990), DOI: 10.1007/BF01099241. Crossref, Google Scholar