On the Dehn functions of Kähler groups

Claudio Llosa Isenrich; Romain Tessera

doi:10.4171/GGD/551

On the Dehn functions of Kähler groups

Claudio Llosa Isenrich
, Romain Tessera

C/o Faculty of Mathematics of the University of Vienna
Université Paris Cité

Research output: Contribution to journal › Article › peer-review

Abstract

We address the problem of which functions can arise as Dehn functions of Kähler groups. We explain why there are examples of Kähler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an example of a Kähler group which has Dehn function bounded below by a cubic function and above by n⁶. As a consequence we obtain that for a compact Kähler manifold having non-positive holomorphic bisectional curvature does not imply having quadratic Dehn function.

Original language	English
Pages (from-to)	469-488
Number of pages	20
Journal	Groups, Geometry, and Dynamics
Volume	14
Issue number	2
DOIs	https://doi.org/10.4171/GGD/551
Publication status	Published - 1 Jan 2020
Externally published	Yes

Keywords

Dehn functions
Isoperimetric functions
Kähler manifolds and groups

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10.4171/GGD/551

Cite this

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abstract = "We address the problem of which functions can arise as Dehn functions of K{\"a}hler groups. We explain why there are examples of K{\"a}hler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an example of a K{\"a}hler group which has Dehn function bounded below by a cubic function and above by n6. As a consequence we obtain that for a compact K{\"a}hler manifold having non-positive holomorphic bisectional curvature does not imply having quadratic Dehn function.",

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AU - Tessera, Romain

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N2 - We address the problem of which functions can arise as Dehn functions of Kähler groups. We explain why there are examples of Kähler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an example of a Kähler group which has Dehn function bounded below by a cubic function and above by n6. As a consequence we obtain that for a compact Kähler manifold having non-positive holomorphic bisectional curvature does not imply having quadratic Dehn function.

AB - We address the problem of which functions can arise as Dehn functions of Kähler groups. We explain why there are examples of Kähler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an example of a Kähler group which has Dehn function bounded below by a cubic function and above by n6. As a consequence we obtain that for a compact Kähler manifold having non-positive holomorphic bisectional curvature does not imply having quadratic Dehn function.

KW - Dehn functions

KW - Isoperimetric functions

KW - Kähler manifolds and groups

U2 - 10.4171/GGD/551

DO - 10.4171/GGD/551

M3 - Article

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JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

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On the Dehn functions of Kähler groups

Abstract

Keywords

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