JournalsqtVol. 2, No. 2pp. 183–215

HOMFLY-PT polynomial and normal rulings of Legendrian solid torus links

  • Dan Rutherford

    Duke University, Durham, USA
HOMFLY-PT polynomial and normal rulings of Legendrian solid torus links cover
Download PDF

Abstract

We show that for any Legendrian link LL in the 1-jet space of S1S^1 the 2-graded ruling polynomial, RL2(z)R^2_L(z), is determined by the Thurston--Bennequin number and the HOMFLY-PT polynomial. Specifically, we recover RL2(z)R^2_L(z) as a coefficient of a particular specialization of the HOMFLY-PT polynomial. Furthermore, we show that this specialization may be interpreted as the standard inner product on the algebra of symmetric functions that is often identified with a certain subalgebra of the HOMFLY-PT skein module of the solid torus.

In contrast to the 2-graded case, we are able to use 0-graded ruling polynomials to distinguish many homotopically non-trivial Legendrian links with identical classical invariants.

Cite this article

Dan Rutherford, HOMFLY-PT polynomial and normal rulings of Legendrian solid torus links. Quantum Topol. 2 (2011), no. 2, pp. 183–215

DOI 10.4171/QT/19