Topological Quantum Field Theory Seminar

Meridional essential surfaces of unbounded Euler characteristics in knot exteriors

In this talk we will discuss further the existence of knot exteriors 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 exterior contains meridional essential surfaces of simultaneously unbounded genus and number of boundary components. In particular, we construct examples of knot exteriors each of which having all possible compact surfaces embedded as meridional essential surfaces.