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- Title
Poincaré inequalities, embeddings, and wild groups.
- Authors
Naor, Assaf; Silberman, Lior
- Abstract
We present geometric conditions on a metric space (Y,dY) ensuring that, almost surely, any isometric action on Y by Gromov’s expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity of nonlinear Poincaré inequalities, and they are stable under natural operations such as scaling, Gromov–Hausdorff limits, and Cartesian products. We use methods from metric embedding theory to establish the validity of these conditions for a variety of classes of metric spaces, thus establishing new fixed point results for actions of Gromov’s ‘wild groups’.
- Subjects
MATHEMATICAL inequalities; EMBEDDINGS (Mathematics); GROUP theory; POINCARE maps (Mathematics); FIXED point theory; METRIC spaces; ISOMETRICS (Mathematics)
- Publication
Compositio Mathematica, 2011, Vol 147, Issue 5, p1546
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X11005343