No Access

Links and cycles in Dehn quandle homology I: Torus links

Joel Zablow

Joel Zablow

Department of Mathematics, Long Island University, Brooklyn Campus, 1 University Plaza, Brooklyn, New York 11201, USA

Search for more papers by this author

https://doi.org/10.1142/S0218216514500126Cited by:1 (Source: Crossref)

Abstract

We examine some questions regarding which torus links admit colorings by elements of a Dehn quandle.

Keywords:

AMSC: 57Mxx, 17Dxx

References

C. Adams , The Knot Book ( W. H. Freeman , 1994 ) . Google Scholar
Carter, S. Kamada and M. Saito, Geometric interpretations of quandle homology, preprint (2000) , arXiv:math.GT/0006115v1 . Google Scholar
J. S. Carter , S. Kamada and M. Saito , Surfaces in 4-Space , Encyclopedia of Mathematical Sciences 142 ( Springer Verlag , 2004 ) . Crossref, Google Scholar
R. Chamanara, J. Hu and J. Zablow, Extending the Dehn quandle to shears and foliations on the torus, to appear in Fund. Math . Google Scholar
B. Farb and D. Margalit , A Primer on Mapping Class Groups ( Princeton University Press , 2012 ) . Google Scholar
T. Fuller, Cubo A Math. J. 5(3), 275 (2003). Google Scholar
R. Gompf and A. Stipsicz , 4-Manifolds and Kirby Calculus , Graduate Studies in Mathematics 20 ( American Mathematical Society , 1999 ) . Crossref, Google Scholar
D. Joyce, J. Pure Appl. Algebra 23, 37 (1982), DOI: 10.1016/0022-4049(82)90077-9. Crossref, Web of Science, Google Scholar
S. Kamada, Geom. Topol. Monogr. 4, 103 (2002). Google Scholar
L. Kauffman , Knots and Physics , 2nd edn. ( World Scientific , 1993 ) . Crossref, Google Scholar
E. Navas and S. Navas, Osaka J. Math. 45, 973 (2008). Web of Science, Google Scholar
M. Niebrzydowski and J. Przytycki, Osaka J. Math. 46, 645 (2009). Web of Science, Google Scholar
A. Scorpan , The Wild World of 4-Manifolds ( American Mathematical Society , 2005 ) . Google Scholar
D. Yetter, J. Knot Theory Ramifications 12(4), 523 (2003), DOI: 10.1142/S0218216503002597. Link, Web of Science, Google Scholar
J. Zablow, J. Knot Theory Ramifications 12(2), 203 (2003), DOI: 10.1142/S0218216503002391. Link, Web of Science, Google Scholar
J. Zablow, Algebr. Geom. Topol. 8, 101 (2008). Web of Science, Google Scholar
J. Zablow, J. Knot Theory Ramifications 20(12), 1741 (2011), DOI: 10.1142/S0218216511009480. Link, Web of Science, Google Scholar