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arXiv · 0909.3202

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

Koen Struyve
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Abstract

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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Koen Struyve. 2009-09-17. (Non-)completeness of R-buildings and fixed point theorems. https://arxiv.org/abs/0909.3202

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