Is Width Additive?

Is Width Additive?
Ryan Blair, University of California, Santa Barbara
November 17, 2009

Abstract: Width is an invariant of knots that depends on the number of minima and maxima of the knot as well as their relative positions. The behavior of width with respect to connected sum has been studied for three decades. Originally, it was conjectured that width is additive under the operation of connect sum. I will outline classic results pertaining to the question and discuss ongoing joint work with Maggy Tomova that suggests width is not additive.