Title: The Gordon-Litherland pairing, its applications, and some generalizations
Speaker: Micah Chrisman, OSU
Abstract: The Gordon-Litherland pairing has many applications to knot theory and low-dimensional topology. For example, it gives a simple method for computing the signature of a knot. On the other hand, the pairing is isometric to the intersection form of a 2-fold branch cover over the 4-ball with branching set a (possibly non-orientable) spanning surface of the knot. Due to its many applications to knots in the $3$-sphere, there has been recent interest in generalizing the Gordon-Litherland pairing to knots in other $3$-manifolds. In this talk, we give an introduction to the Gordon-Litherland pairing and discuss some of these generalizations. In particular, we consider the case of knots in thickened surfaces $\Sigma \times [0,1]$, where $\Sigma$ is closed and oriented.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for one or two credit hours of Math 6193 with Professor Henri Moscovici.
