On the Dehn functions of K\"ahler groups
Geometric Topology
2019-06-10 v2 Algebraic Geometry
Group Theory
Abstract
We address the problem of which functions can arise as Dehn functions of K\"ahler groups. We explain why there are examples of K\"ahler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an example of a K\"ahler group which has Dehn function bounded below by a cubic function and above by . As a consequence we obtain that for a compact K\"ahler manifold having non-positive holomorphic bisectional curvature does not imply having quadratic Dehn function.
Keywords
Cite
@article{arxiv.1807.03677,
title = {On the Dehn functions of K\"ahler groups},
author = {Claudio Llosa Isenrich and Romain Tessera},
journal= {arXiv preprint arXiv:1807.03677},
year = {2019}
}
Comments
15 pages, V2: Minor corrections and improvements to the exposition. Final accepted version, to appear in Groups, Geometry, and Dynamics