dc.contributor.advisor | Dowdall, Spencer | |
dc.creator | Lorenz, Aidan | |
dc.date.accessioned | 2024-08-15T18:19:25Z | |
dc.date.created | 2024-08 | |
dc.date.issued | 2024-05-14 | |
dc.date.submitted | August 2024 | |
dc.identifier.uri | http://hdl.handle.net/1803/19160 | |
dc.description.abstract | The dynamics of pseudo-Anosov homeomorphisms of surfaces are encapsulated largely by their dilatations. Since Penner's work in the 90's, questions about minimal dilatation pseudo-Anosovs have been an area of active research with progress being made in the past decade in particular by the likes of Hironaka, and Kin-Kojima-Takasawa, among others. An approach which has proven fruitful to the aforementioned authors is to fix a hyperbolic fibered 3-manifold and study the pseudo-Anosov monodromies of its Dehn
fillings. By a theorem of Farb-Leininger-Margalit, all small dilatation pseudo-Anosovs are monodromies of Dehn fillings of finitely many such fully punctured 3-manifolds. In this thesis, we take this approach further by considering entire classes of 3-manifolds at once. In particular, we show that for any hyperbolic fibered 3-manifold M that is either closed or has second betti number less than or equal to 2, the sequence (\delta_g^g(M,F))_g of least dilatations arising as monodromies of Dehn fillings of M across all realizable genera converges. Furthermore, we conjecture and offer a proof method - and
make partial progress on this proof method - that similar strategies could be used to show that the sequence (\delta_g^g)_g of least dilatations across all genera has finitely many accumulation points. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.subject | pseudo-Anosov, dynamics, mapping class groups, dilatations, stretch factors | |
dc.title | Small Dilatation Pseudo-Anosovs Coming from Dehn Fillings of Hyperbolic Fibered 3-Manifolds | |
dc.type | Thesis | |
dc.date.updated | 2024-08-15T18:19:25Z | |
dc.type.material | text | |
thesis.degree.name | PhD | |
thesis.degree.level | Doctoral | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University Graduate School | |
local.embargo.terms | 2025-08-01 | |
local.embargo.lift | 2025-08-01 | |
dc.creator.orcid | 0009-0000-4898-9362 | |
dc.contributor.committeeChair | Dowdall, Spencer | |