Joint GT-UGA Seminar at GT - The ribbon genus of a knotted surface

Geometry Topology Seminar
Monday, October 1, 2018 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 006
Jason Joseph – UGA
Caitlin Leverson
The knot group has played a central role in classical knot theory and has many nice properties, some of which fail in interesting ways for knotted surfaces. In this talk we'll introduce an invariant of knotted surfaces called ribbon genus, which measures the failure of a knot group to 'look like' a classical knot group. We will show that ribbon genus is equivalent to a property of the group called Wirtinger deficiency. Then we will investigate some examples and conclude by proving a connection with the second homology of the knot group.