Third Year Candidacy Requirement: "Minimal genus Seifert surfaces for Montesinos knots"

Abstract: In this talk, I will present the preliminaries for understanding my thesis question. We will discuss the classification of Montesinos knots, described through continued fractions, through their explicit construction of respective Seifert surfaces of minimal genus. We can categorize Montesinos knots into odd or even type, and then place further categorizations of those of even type to minimize the number of cases we consider. Having categorized all Montesinos knots into 4 types, we study their individual and respective Seifert surfaces of minimal genus. The most interesting case will give rise to a special Seifert surface that is not obtained by the usual Seifert algorithm. The goal of my thesis will be to use this classification to improve upon existing work by Delman-Roberts, and then to generalize the results to other settings. 

Host: Rachel Roberts