Homfly Polynomials of Generalized Hopf Links

Abstract

Following the recent work by T.-H. Chan in [HOMFLY polynomial of some generalized Hopf links, J. Knot Theory Ramif. 9 (2000) 865--883] on reverse string parallels of the Hopf link we give an alternative approach to finding the Homfly polynomials of these links, based on the Homfly skein of the annulus. We establish that two natural skein maps have distinct eigenvalues, answering a question raised by Chan, and use this result to calculate the Homfly polynomial of some more general reverse string satellites of the Hopf link.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-2.abs.html

References in corpus (1)

• Idempotents of Hecke algebras of type A

Cited by in corpus (7)

• On colored HOMFLY polynomials for twist knots
• The HOMFLYPT skein algebra of the torus and the elliptic Hall algebra
• String theory and the Kauffman polynomial
• Cabling procedure for the colored HOMFLY polynomials
• Integrality of Homfly (1,1)-tangle invariants
• Full Colored HOMFLYPT Invariants, Composite Invariants and Congruent Skein Relation
• The Ropelength of Complex Knots