No Access

FIRST NON-VANISHING SELF-LINKING OF KNOT (III) MASSEY–MILNOR THEORY

CHUN-CHUNG HSIEH

Institute of Mathematics, Academia Sinica, Nankang, Taipei 115, Taiwan

https://doi.org/10.1142/S0218216511008929Cited by:1 (Source: Crossref)

Abstract

In this paper, following the scheme of [11–13, 16, 17], we study the first non-vanishing self-linkings of knots in both combinatoric and diagrammatic aspects. The method of attack comes from Massey–Milnor linking theory.

Keywords:

AMSC: 57M25

References

Y. Akutsu, T. Deguchi and M. Wadati, J. Phys. Soc. Japan 56, 3464 (1987). Crossref, Google Scholar
Y. Akutsu, T. Deguchi and M. Wadati, J. Phys. Soc. Japan 57, 1173 (1987). Crossref, Google Scholar
M. F. Atiyak , The Geometry and Physics of Knots ( Cambridge University Press , 1990 ) . Crossref, Google Scholar
Y. Akutsu and M. Wadati, Commun. Math. Phys. 117, 243 (1988), DOI: 10.1007/BF01223592. Crossref, Web of Science, Google Scholar
Y. Akutsu and M. Wadati, J. Phys. Soc. Japan 56, 3039 (1987). Crossref, Google Scholar
Y. Akutsu and M. Wadati, J. Phys. Soc. Japan 56, 839 (1987). Crossref, Google Scholar
T. Deguchi, Y. Akutsu and M. Wadati, J. Phys. Soc. Japan 57, 757 (1988). Crossref, Google Scholar
T. Deguchi, M. Wadati and Y. Akutsu, J. Phys. Soc. Japan 57, 1905 (1988). Crossref, Google Scholar
R. Fenn , Techniques of Geometric Topology ( Cambridge University Press , 1983 ) . Google Scholar
C. C. Hsieh, J. Knot Theory Ramifications 16, 1235 (2007). Link, Web of Science, Google Scholar
C. C. Hsieh, J. Knot Theory Ramifications 17, 877 (2008). Link, Web of Science, Google Scholar
C. C. Hsieh, First non-vanishing self-linkings of knots (I), Combin. Diagram. Study, preprint . Google Scholar
C. C. Hsieh, First non-vanishing self-linkings of knots (II), Chern-Simons-Witten Theory, preprint . Google Scholar
C. C. Hsieh, First non-vanishing self-linkings of knots (IV), Massey-Milnor linking = Chern-Simons-Witten graphs, preprint . Google Scholar
J. Hebda, C. C. Hsieh and M. Tsau, Canad. Math. Bull. 50, 390 (2007), DOI: 10.4153/CMB-2007-037-8. Crossref, Web of Science, Google Scholar
C. C. Hsieh, L. H. Kauffman and M. C. Tsau, Massey-Milnor linking in knot theory, preprint . Google Scholar
C. C. Hsieh and S. W. Yang, J. Knot Theory Ramifications 14, 689 (2005). Link, Web of Science, Google Scholar
W. S. Massey, Higher order linking numbers, Conf. Algebraic Topology (University of Illinois, Chicago Circle, 1969) pp. 174–205. Google Scholar
J. Milnor, Ann. Math. 59, 177 (1954), DOI: 10.2307/1969685. Crossref, Web of Science, Google Scholar
J. Milnor, Isotopy of links, Algebraic Geometry and Topology, A Symposium in Honor of S. Lefschetz (Princeton University Press, 1957) pp. 280–306. Google Scholar
R. Porter, Trans. Amer. Math. Soc. 257, 39 (1980). Web of Science, Google Scholar
E. Witten, Commun. Math. Phys. 121, 351 (1989), DOI: 10.1007/BF01217730. Crossref, Web of Science, Google Scholar
M. Wadati, T. Deguchi and Y. Akutsu, Exactly solvable models and knot theory, Phys. Reports 180 (1989) 247–332 . Google Scholar