University of Arkansas Topology Seminar: 4/24/2014

Speaker: Trent Schrimer

Title: Knots with high distance free decompositions

Abstract: I define the notion of a high distance free decomposition and show that many knots admit high distance free decompositions. A large class of these knots have interesting properties: their tunnel number has high degeneration under the operation of connected sum (with certain other kinds of knots), they admit multiple minimal genus Heegaard splittings, some strongly irreducible, some weakly reducible. They also have interesting surgery properties and group theoretic properties which I will discuss. This work is joint with Jesse Johnson.