Date of Graduation
5-2017
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
Yo'av Rieck
Committee Member
Jeremy Van-Horn Morris
Second Committee Member
Matt Clay
Keywords
Pure sciences, Euler, Surface homeomorphisms, Surfaces
Abstract
The goal of this paper is to show for a compact triangulated 3-manifold M with boundary which fibers over the circle that whenever F is a fiber with sufficiently negative Euler characteristic the monodromymaps an essential simple closed curve or an essential simple arc in F to be disjoint from its image (possibly after isotopy). This is shown by applying the theorem of Ichihara, Kobayashi, and Rieck in [10] to the double of M to get a pair of pants. We then find an equivariant pair of pants and use it to find an essential simple closed curve or an essential simple arc which satisfies our theorem. As a corollary, if we add the hypothesis that M is a hyperbolic manifold, we get that the translation distance of the monodromy in the arc and curve complex of F is at most 1 for all but finitely many monodromy maps.
Citation
Harris, M. (2017). 3-Manifold Perspective on Surface Homeomorphisms for Surfaces with Very Negative Euler Characteristic. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/1909