Geodesic
(Non)-completeness of $ℝ$-buildings and fixed point theorems
Koen Struyve1
1Universiteit Gent, Belgium
Groups, geometry, and dynamics, Tome 5 (2011) no. 1, pp. 177-188

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DOI

We prove two generalizations of results of Bruhat and Tits involving metrical completeness and R-buildings. Firstly, we give a generalization of the Bruhat–Tits fixed point theorem also valid for non-complete R-buildings with the added condition that the group is finitely generated. Secondly, we generalize a criterion which reduces the problem of completeness to the wall trees of the R-building. This criterion was proved by Bruhat and Tits for R-buildings arising from root group data with valuation.
DOI : 10.4171/ggd/121
Classification : 51-XX, 20-XX, 00-XX
Mots-clés : Euclidean buildings, fixed point theorems, metric completeness

Koen Struyve  1

1 Universiteit Gent, Belgium 
Koen Struyve. (Non)-completeness of $ℝ$-buildings and fixed point theorems. Groups, geometry, and dynamics, Tome 5 (2011) no. 1, pp. 177-188. doi: 10.4171/ggd/121
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/121/}
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