Complexity of 3-manifolds obtained by Dehn filling

Abstract

Let M be a compact 3-manifold with boundary a single torus. We present upper and lower complexity bounds for closed 3-manifolds obtained as even Dehn fillings of M. As an application, we characterise some infinite families of even Dehn fillings of M for which our method determines the complexity of their members up to an additive constant. The constant only depends on the size of a chosen triangulation of M, and the isotopy class of its boundary. We then show that, given a triangulation T of M with 2-triangle torus boundary, there exist infinite families of even Dehn fillings of M for which we can determine the complexity of the filled manifolds with a gap between upper and lower bounds of a..