Lipschitz connectivity and filling invariants in solvable groups and buildings

Research output: Contribution to journalArticle

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 Sol2n+1, horospheres in euclidean buildings, Hilbert modular groups and certain S–arithmetic groups.

Original languageEnglish (US)
Pages (from-to)2375-2417
Number of pages43
JournalGeometry and Topology
Volume18
Issue number4
DOIs
StatePublished - Oct 2 2014

Fingerprint

Solvable Group
Lipschitz
Connectivity
Invariant
Dehn Function
Horosphere
Semisimple Groups
Extension Theorem
Modular Group
Sharp Bound
Finiteness
Hilbert
Euclidean
Ball
Subspace
Higher Order
Subset
Buildings

Keywords

  • Filling invariants
  • Lattices in arithmetic groups
  • Lipschitz extensions

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Lipschitz connectivity and filling invariants in solvable groups and buildings. / Young, Robert.

In: Geometry and Topology, Vol. 18, No. 4, 02.10.2014, p. 2375-2417.

Research output: Contribution to journalArticle

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