Volume 18, issue 4 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23, 1 issue

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Lipschitz connectivity and filling invariants in solvable groups and buildings

Robert Young

Geometry & Topology 18 (2014) 2375–2417

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.

filling invariants, Lipschitz extensions, lattices in arithmetic groups
Mathematical Subject Classification 2010
Primary: 20F65, 20E42
Received: 2 April 2013
Accepted: 11 January 2014
Published: 2 October 2014
Proposed: Martin R Bridson
Seconded: Steve Ferry, Walter Neumann
Robert Young
Department of Mathematics
University of Toronto
40 St. George St., Room 6290
Toronto, Ontario M5S 2E4