### 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.

BACK TO SCHEDULE