Georgia Institute of Technology College of Sciences

Normal rulings are decompositions of a projection of a Legendrian knot or link. Not every link has a normal ruling, so existence of a normal ruling gives a Legendrian link invariant. However, one can use the normal rulings of a link to define the ruling polynomial of a link, which is a more useful Legendrian knot invariant. In this talk, we will discuss normal rulings of Legendrian links in various manifolds and prove that the ruling polynomial is a Legendrian link invariant.