Special issue: 2014 KOOK-TAPU Workshop on Knot Theory and Related TopicsNo Access

Applying Lipson's state models to marked graph diagrams of surface-links

Yewon Joung

Department of Mathematics, Graduate School of Natural Sciences, Pusan National University, Busan 609-735, Korea

Search for more papers by this author

Seiichi Kamada

Department of Mathematics, Osaka City University, Osaka 558-8585, Japan

Search for more papers by this author

, and

Sang Youl Lee

Department of Mathematics, Pusan National University, Busan 609-735, Korea

Search for more papers by this author

https://doi.org/10.1142/S0218216515400039Cited by:5 (Source: Crossref)

Abstract

A. S. Lipson constructed two state models yielding the same classical link invariant obtained from the Kauffman polynomial F(a, u). In this paper, we apply Lipson's state models to marked graph diagrams of surface-links, and observe when they induce surface-link invariants.

Keywords:

AMSC: 57Q45, 57M25

References

M. Asada , Kobe J. Math. 18 , 163 ( 2001 ) . Google Scholar
R. H. Fox, Topology of 3-manifolds and Related Topics (Prentice-Hall, Englewood Cliffs, NJ, 1962) pp. 120–167. Google Scholar
Y. Joung, J. Kim and S. Y. Lee, J. Knot Theory Ramifications 22(9), 25 (2013). Link, Web of Science, Google Scholar
S. Kamada , Osaka J. Math. 26 , 367 ( 1989 ) . Web of Science, Google Scholar
S. Kamada , Braid and Knot Theory in Dimension Four , Mathematical Surveys and Monographs 95 ( American Mathematical Society , Providence, RI , 2002 ) . Crossref, Google Scholar
A. Kawauchi , A Survey of Knot Theory ( Birkhäuser , 1996 ) . Google Scholar
A. Kawauchi , T. Shibuya and S. Suzuki , Math. Sem. Notes Kobe Univ. 10 , 75 ( 1982 ) . Google Scholar
C. Kearton and V. Kurlin , Algebr. Geom. Topol. 8 , 1223 ( 2008 ) . Crossref, Web of Science, Google Scholar
J. Kim, Y. Joung and S. Y. Lee, J. Knot Theory Ramifications 24(4), 1550018-1 (2015). Google Scholar
S. Y. Lee, Intelligence of Low Dimensional Topology, Series on Knots Everything 40 (World Scientific, Hackensack, NJ, 2007) pp. 189–196. Link, Google Scholar
S. Y. Lee , J. Knot Theory Ramifications 17 , 439 ( 2008 ) . Link, Web of Science, Google Scholar
S. Y. Lee , Trans. Amer. Math. Soc. 361 , 237 ( 2009 ) . Crossref, Web of Science, Google Scholar
A. S. Lipson , Pacific J. Math. 152 , 337 ( 1992 ) . Crossref, Web of Science, Google Scholar
S. J. Lomonaco Jr. , Pacific J. Math. 95 , 349 ( 1981 ) . Crossref, Web of Science, Google Scholar
M. Soma , Topology Appl. 121 , 231 ( 2002 ) . Crossref, Web of Science, Google Scholar
F. J. Swenton , J. Knot Theory Ramifications 10 , 1133 ( 2001 ) . Link, Web of Science, Google Scholar
K. Yoshikawa , Osaka J. Math. 31 , 497 ( 1994 ) . Web of Science, Google Scholar