Bridge trisections of knotted surfaces in the foursphere
Bridge trisections of knotted surfaces in the foursphere

Jeffrey Meier , University of Indiana
Fine Hall 314
A trisection is a decomposition of a fourmanifold into three trivial pieces and serves as a fourdimensional analogue to a Heegaard decomposition of a threemanifold. In this talk, I will discuss an adaptation of the theory of trisections to the relative setting of knotted surfaces in the foursphere that serves as a fourdimensional analogue to bridge splittings of classical knots and links  every such surface admits a decomposition into three standard pieces called a bridge trisection. I'll describe how every such decomposition can be represented diagrammatically as a triple of trivial tangles and give a calculus of moves for passing between diagrams of a fixed surface. This is joint work with Alexander Zupan.