Geodesic
Properly discontinuous actions versus uniform embeddings
Kevin Schreve1 orcid
1University of Chicago, USA
Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 1015-1039

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DOI

Whenever a finitely generated group G acts properly discontinuously by isometries on a metric space X, there is an induced uniform embedding (a Lipschitz and uniformly proper map) ρ:G→X given by mapping G to an orbit. We study when there is a difference between a finitely generated group G acting properly on a contractible n-manifold and uniformly embedding into a contractible n-manifold. For example, Kapovich and Kleiner showed that there are torsion-free hyperbolic groups that uniformly embed into a contractible 3-manifold but do not act on a contractible 3-manifold. We show that k-fold products of certain examples do not act on contractible 3k-manifolds.
DOI : 10.4171/ggd/621
Classification : 11-XX, 57-XX
Mots-clés : Van Kampen obstruction, Wu invariant, uniformly proper dimension, action dimension

Kevin Schreve  1

1 University of Chicago, USA 
Kevin Schreve. Properly discontinuous actions versus uniform embeddings. Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 1015-1039. doi: 10.4171/ggd/621
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     pages = {1015--1039},
     year = {2021},
     volume = {15},
     number = {3},
     doi = {10.4171/ggd/621},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/621/}
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