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AMPHICHEIRAL LINKS WITH SPECIAL PROPERTIES, I

TERUHISA KADOKAMI

Department of Mathematics, East China Normal University, Dongchuan-lu 500, Shanghai 200241, China

https://doi.org/10.1142/S0218216511010000Cited by:0 (Source: Crossref)

Abstract

We provide necessary conditions for the Alexander polynomials of algebraically split component-preservingly amphicheiral links. We raise a conjecture that the Alexander polynomial of an algebraically split component-preservingly amphicheiral link with even components is zero. Our necessary conditions and some examples support the conjecture.

Dedicated to Professor Akio Kawauchi for his 60th birthday

Keywords:

AMSC: 57M25, 57M27

References

D. Bar-Natan and S. Morrison, Knot atlas, http://katlas.math.toronto.edu/wiki/Main_Page . Google Scholar
F. Bonahon and L. C. Siebenmann, New geometric splittings of classical knots and the classification and symmetries of arborescent knots, http://www-bcf.usc.edu/fbonahon/Research/Preprints/BonSieb.pdf . Google Scholar
R. Hartley, Math. Ann. 252, 103 (1980), DOI: 10.1007/BF01420117. Crossref, Web of Science, Google Scholar
R. Hartley and A. Kawauchi, Math. Ann. 243, 63 (1979), DOI: 10.1007/BF01420207. Crossref, Web of Science, Google Scholar
J. Hillman, Kobe J. Math. 3, 7 (1986). Google Scholar
B. Jianget al., Topology Appl. 119, 185 (2002), DOI: 10.1016/S0166-8641(01)00062-1. Crossref, Web of Science, Google Scholar
T. Kadokami, J. Knot Theory Ramifications 20, 1129 (2011). Link, Web of Science, Google Scholar
T. Kadokami, J. Knot Theory Ramifications 21(6), 15 (2012). Web of Science, Google Scholar
T. Kadokami, Finite slope surgeries along the Milnor links, in preparation . Google Scholar
T. Kadokami and A. Kawauchi, Sci. China Math. 54, 2213 (2011), DOI: 10.1007/s11425-011-4217-6. Crossref, Web of Science, Google Scholar
T. Kadokami, N. Maruyama and M. Shimozawa, Lens surgeries along the n-twisted Whitehead link, to appear in Kyungpook Math. J . Google Scholar
T. Kanenobu, J. Austral. Math. Soc. (Ser. A) 36, 59 (1984), DOI: 10.1017/S1446788700027336. Crossref, Google Scholar
A. Kawauchi, Invent. Math. 43, 177 (1977), DOI: 10.1007/BF01390003. Crossref, Web of Science, Google Scholar
A. Kawauchi, Proc. Japan Acad. Ser. A Math. Sci. 55, 399 (1979), DOI: 10.3792/pjaa.55.399. Crossref, Google Scholar
A. Kawauchi , A Survey of Knot Theory ( Birkhäuser , 1996 ) . Google Scholar
A. Kawauchi, Low Dimensional Topology, Contemporary Mathematics 233 (American Mathematical Society, 1999) pp. 97–116. Crossref, Google Scholar
S. Kojima and M. Yamasaki, Invent. Math. 54, 213 (1979), DOI: 10.1007/BF01390230. Crossref, Web of Science, Google Scholar
J. Milnor, Ann. Math. (2) 59, 177 (1954), DOI: 10.2307/1969685. Crossref, Web of Science, Google Scholar
J. Milnor, Ann. Math. (2) 76, 137 (1962), DOI: 10.2307/1970268. Crossref, Web of Science, Google Scholar
T. Sakai, Math. Ann. 266, 229 (1983), DOI: 10.1007/BF01458444. Crossref, Web of Science, Google Scholar
G. Torres, Ann. Math. (2) 57, 57 (1953), DOI: 10.2307/1969726. Crossref, Web of Science, Google Scholar
V. Turaev, Russian Math. Surveys 41(1), 119 (1986), DOI: 10.1070/RM1986v041n01ABEH003204. Crossref, Web of Science, Google Scholar
S. Wang, Acta Math. Sinica 24, 997 (2008), DOI: 10.1007/s10114-007-6372-9. Crossref, Web of Science, Google Scholar
W. Whitten, Trans. Amer. Math. Soc. 135, 213 (1969), DOI: 10.1090/S0002-9947-1969-0242146-4. Crossref, Web of Science, Google Scholar