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

2009/09/17 by Koen Struyve, Struyve, Koen · 1 citation
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.0909.3202

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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