三维映射环面的整填充体积、复杂度与整单纯体积
几何拓扑
2024-10-04 v2 代数拓扑
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摘要
我们证明闭定向曲面上 Dehn twist 的整填充体积为零，即具有单同调 的映射环面的整单纯体积关于 次线性增长。我们推导出具有零整填充体积的曲面上映射类的完全刻画，并基于 Purcell 与 Lackenby 关于映射环面复杂度的结果，证明在三维中复杂度与整单纯体积不是 Lipschitz 等价的。
引用
@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}
}
备注
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