(Non-)completeness of R-buildings and fixed point theorems

Details (Non-)completeness of R-buildings and fixed point theorems (Non-)completeness of R-buildings and fixed point theorems

2009-09-17

arxiv.org/abs/0909.3202v1

Mathematics

Metric Geometry

Scientific paper

We prove two generalizations of results proved by 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, but 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.

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