Geometry & Topology

Lipschitz connectivity and filling invariants in solvable groups and buildings

Robert Young

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Filling invariants of a group or space are quantitative versions of finiteness properties which measure the difficulty of filling a sphere in a space with a ball. Filling spheres is easy in nonpositively curved spaces, but it can be much harder in subsets of nonpositively curved spaces, such as certain solvable groups and lattices in semisimple groups. In this paper, we give some new methods for bounding filling invariants of such subspaces based on Lipschitz extension theorems. We apply our methods to find sharp bounds on higher-order Dehn functions of Sol2n+1, horospheres in euclidean buildings, Hilbert modular groups and certain S–arithmetic groups.

Article information

Geom. Topol., Volume 18, Number 4 (2014), 2375-2417.

Received: 2 April 2013
Accepted: 11 January 2014
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20E42: Groups with a $BN$-pair; buildings [See also 51E24]

filling invariants Lipschitz extensions lattices in arithmetic groups


Young, Robert. Lipschitz connectivity and filling invariants in solvable groups and buildings. Geom. Topol. 18 (2014), no. 4, 2375--2417. doi:10.2140/gt.2014.18.2375.

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