Title: Bridge Number and Conway Products
Abstract: A well known theorem of Schubert tells us that the bridge number of knots is additive with respect to the cut and paste operation of connected sum. The Conway product is a vast generalization of connected sum achieved by removing rational tangles and gluing along 4-punctured spheres. In this talk, we will present a lower bound for the bridge number of a Conway product in terms of the bridge number of the factor knots. Additionally, we will present examples which show this lower bound is sharp.