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KAUFFMAN BRACKET SKEIN MODULE OF THE CONNECTED SUM OF TWO PROJECTIVE SPACES

MACIEJ MROCZKOWSKI

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

https://doi.org/10.1142/S0218216511008905Cited by:16 (Source: Crossref)

Abstract

Diagrams and Reidemeister moves for links in a twisted S¹-bundle over an unorientable surface are introduced. Using these diagrams, we compute the Kauffman Bracket Skein Module (KBSM) of ℝP³♯ℝP³. In particular, we show that it has torsion. We also present a new computation of the KBSM of S¹ × S² and the lens spaces L(p, 1).

Keywords:

AMSC: 57M27

References

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
L. H. Kauffman, Topology 26(3), 395 (1987). Crossref, Web of Science, 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
J. H. Przytycki, Bull. Polish Acad. Sci. 39(1–2), 91 (1991). Google Scholar
V. G. Turaev, J. Soviet Math. 52, 2799 (1990), DOI: 10.1007/BF01099241. Crossref, Google Scholar