Bridge trisections of knotted surfaces in the four-sphere

Series: 
Geometry Topology Seminar
Thursday, December 3, 2015 - 14:00
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
University of Indiana
Organizer: 

Please not non-standard day for seminar. 

A trisection is a decomposition of a four-manifold into three trivial pieces and serves as a four-dimensional analogue to a Heegaard decomposition of a three-manifold.  In this talk, I will discuss an adaptation of the theory of trisections to the relative setting of knotted surfaces in the four-sphere that serves as a four-dimensional analogue to bridge splittings of classical knots and links.  I'll show that every such surface admits a decomposition into three standard pieces called a bridge trisection.  I'll also 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.‚Äč