Meridional essential surfaces of unbounded Euler characteristics in knot complements

Geometric Structures on 3-manifolds
Topic:Meridional essential surfaces of unbounded Euler characteristics in knot complements
Speaker:João Nogueira
Affiliation:University of Coimbra
Date:Wednesday, April 20
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/geostruct/2016/0420-Nogueira

In this talk we will discuss further the existence of knot complements with essential surfaces of unbounded Euler characteristics. More precisely, we show the existence of a knot with an essential tangle decomposition for any number of strings. We also show the existence of knots where each complement contains meridional essential surfaces of simultaneously unbounded genus and number of boundary components. In particular, we construct examples of knot complements each of which having all possible compact surfaces embedded as meridional essential surfaces.