Knots in Handlebodies, Bongles, and Hyperbolic Volume by Lizzie High ’24

Knots in Handlebodies, Bongles, and Hyperbolic Volume by Lizzie High ’24, Monday April 29, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Thesis

In this presentation, we will explore the notion of hyperbolic volume in staked knots. We begin by studying the realization of hyperbolic staked knots as knots living in doubled higher genus surfaces.  In particular, we define and examine a class of staked knots called “charm bracelets”, with a specific interest in a subset of such knots we call “bongles”.  We prove that bongles are hyperbolic if and only if they are alternating. Further, we extend the bongle class to multi-lobed bongles and mixed multi-lobed bongles, and bound the volumes of these objects.