Lipschitz connectivity and filling invariants in solvable groups and buildings

Young, Robert

doi:10.2140/gt.2014.18.2375

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Lipschitz connectivity and filling invariants in solvable groups and buildings

Robert Young

Geometry & Topology 18 (2014) 2375–2417

DOI: 10.2140/gt.2014.18.2375

Correction: 10.2140/gt.2016.20.2433

Abstract

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 ${Sol}_{2 n + 1}$ , horospheres in euclidean buildings, Hilbert modular groups and certain $S$ –arithmetic groups.

Keywords

filling invariants, Lipschitz extensions, lattices in arithmetic groups

Mathematical Subject Classification 2010

Primary: 20F65, 20E42

References

Publication

Received: 2 April 2013

Accepted: 11 January 2014

Published: 2 October 2014

Proposed: Martin R Bridson

Seconded: Steve Ferry, Walter Neumann

Correction: 15 September 2016

Authors

Robert Young
Department of Mathematics University of Toronto 40 St. George St., Room 6290 Toronto, Ontario M5S 2E4 Canada

Volume 18, issue 4 (2014)