Malcolm Gabbard:

Triplane diagrams and band diagrams are two common ways to depict embedded surfaces in 4-manifolds. We will briefly review how to construct and use both diagrams to depict surfaces in the 4-sphere up to isotopy. Combining these notions, we introduce a new diagrammatic approach to studying 3-manifolds in the 5-sphere. In this talk we will cover the basic approach for the banded triplane diagrams as well as preliminary results and ongoing work.