Joan E. Licata

Joan E. Licata

Research

Papers

We partially compute the Heegaard Floer link invariant of (n,n) torus links and give a conjecture for the complete invariant. This paper has several open questions; please let me know if you answer them!

(arXiv1208:0394)

We define a contact homology-type invariant for Legendrian knots in Seifert fibered spaces equipped with transverse, S1-invariant contact structures.

(To appear in Quantum Topology, joint with J. Sabloff)

We construct rational Seifert surfaces for knots in Seifert fibered spaces. As an application, we give combinatorial formulae for computing the rational Thurston-Bennequin and rotation numbers of rationally null-homologous knots in contact Seifert fibered spaces.

Pacific Journal of Mathematics 258-1 (2012), 1990221, joint with J. Sabloff.

We relate the front and Lagrangian projections of grid number one knots in lens spaces, and we use this correspondence to determine the existence of augmentations of the Legendrian contact homology DGA.

The Mathematics of Knots: Theory and Application (Computations in Mathematical and Computational Sciences), edited by Markus Banagl and Denis Vogel, Springer (2010) 143-168. The original publication is available at www.springerlink.com.

Viewing lens spaces as quotients of circle-bundles, we construct a combinatorially-defined differential algebra whose homology is an invariant of the Legendrian isotopy class of K.

Communications in Contemporary Mathematics, Vol. 13, No.1, 91-121.

This paper presents new algorithms for constructing Seifert surfaces for knots and links in the three-sphere. We apply the main algorithm to a knot whose canonical genus is less than its Seifert genus and show that the surface constructed realizes the canonical genus.

Journal of Knot Theory and Its Ramifications, Volume 19, Issue 2 (2010)

We use the Heegaard Floer link invariant to determine the Thurston polytopes of a members of a four-parameter family of pretzel links. This family includes an infinite set of links with vanishing multivariable Alexander polynomial.

Algebraic and Geometric Topology, 8 (2008)