Hyperbolic 3-manifolds of bounded volume and trace field degree

Hyperbolic 3-Manifolds;Volume;Dehn Filling;Trace Field

Jeon, Bo Gwang

关键词: Hyperbolic 3-Manifolds;    Volume;    Dehn Filling;    Trace Field;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/45424/Bo%20Gwang_Jeon.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

For a single cusped hyperbolic 3-manifold, Hodgson proved that there are only finitely many Dehnfillingsof it whose tracefields have bounded degree. In this paper, we conjecture the same for manifolds with morecusps, and give the first positive results in this direction. For example, in the 2-cusped case, if a manifoldhas linearly independent cusp shapes, we show that the manifold has the desired property. To prove theresults, we use Habegger's proof of the Bounded Height Conjecture in arithmetic geometry.