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Extending unknotting operations to Seifert surfaces


Speaker: Carson Rogers, UC Davis
Location: 2112 MSB
Start time: Tue, May 29 2018, 1:10PM

Title: Extending unknotting operations to Seifert surfaces

Abstract: This talk will surround the study of crossing changes on knots which extend to twisting operations on their minimum-genus Seifert surfaces. To motivate the subject, I will begin with an overview of the role that this study played in Kobayashi's characterization of unknotting number one fibered knots, and in Kalfagianni's work on the nugatory crossing conjecture. We will then turn to a question posed fairly recently by Baader and Dehornoy: which genus g fibered knots can be unknotted by a sequence of g crossing changes which "untwist" the fiber surface in a suitable sense? After explaining exactly what this means and the context in which the question arose, I will show why Kobayashi's work implies that unknotting number one fibered knots fall into this category, and discuss the progress made on this question in my thesis.