Talk by Adam Howard (Mathematical Sciences' Graduate Student, MSU)

9/23/2019  Wilson Hall 1-144  4:10-5:00pm

Abstract:  Knots are a common object, they seem to appear every time we take our headphones out of our pocket. In this talk, we will explore some binary operations one can perform on knots. In particular, we will focus on the satellite knot construction and see that the connect-sum of knots is a special case of this construction. Satellite knots behave well with respect to a knot invariant called bridge number, and for the case of connect-sum, bridge number is additive. These results were originally proven by Horst Schubert in the 50s, but more recently Jennifer Schultens has given an original and modern proof using Morse theory. This new perspective can be utilized in exploring knots of higher dimension and may produce similar results.