Brendan Owens, Slice surfaces and double-branched covers

Abstract: Gordon and Litherland defined a bilinear form on the first homology of an embedded surface in the 3–sphere, and used it to give a formula for the signature of the bounding link. I will describe a generalisation of this to embedded surfaces in the 4–ball. I will also discuss how this may be useful in searching for ribbon alternating knots. This is based on joint work with Greene and Strle, and also joint work with Swenton.