Integral filling volume, complexity and integral simplicial volume of 3-dimensional mapping tori
Abstract
We show that the integral filling volume of a Dehn twist on a closed oriented surface vanishes, i.e. that the integral simplicial volume of the mapping torus with monodromy grows sublinearly with respect to . We deduce a complete characterization of mapping classes on surfaces with vanishing integral filling volume and, building on results by Purcell and Lackenby on the complexity of mapping tori, we show that, in dimension three, complexity and integral simplicial volume are not Lipschitz equivalent.
Keywords
Cite
@article{arxiv.2303.07730,
title = {Integral filling volume, complexity and integral simplicial volume of 3-dimensional mapping tori},
author = {Federica Bertolotti and Roberto Frigerio},
journal= {arXiv preprint arXiv:2303.07730},
year = {2024}
}
Comments
Section 4 from version 1 has been removed, since a better look at the literature allowed us to observe that integral simplicial volume is not finite-to-one in dimension bigger than 3. Other minor corrections have been performed. Accepted for publication in Groups, Geometry and Dynamics