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

Koen Struyve (UGent)
(2011) GROUPS GEOMETRY AND DYNAMICS. 5(1). p.177-188
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Abstract
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.
Keywords
metric completeness, POLYGONS, Euclidean buildings, fixed point theorems

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MLA
Struyve, Koen. “(Non)-Completeness of ℝ-Buildings and Fixed Point Theorems.” GROUPS GEOMETRY AND DYNAMICS, vol. 5, no. 1, 2011, pp. 177–88, doi:10.4171/GGD/121.
APA
Struyve, K. (2011). (Non)-completeness of ℝ-buildings and fixed point theorems. GROUPS GEOMETRY AND DYNAMICS, 5(1), 177–188. https://doi.org/10.4171/GGD/121
Chicago author-date
Struyve, Koen. 2011. “(Non)-Completeness of ℝ-Buildings and Fixed Point Theorems.” GROUPS GEOMETRY AND DYNAMICS 5 (1): 177–88. https://doi.org/10.4171/GGD/121.
Chicago author-date (all authors)
Struyve, Koen. 2011. “(Non)-Completeness of ℝ-Buildings and Fixed Point Theorems.” GROUPS GEOMETRY AND DYNAMICS 5 (1): 177–188. doi:10.4171/GGD/121.
Vancouver
1.
Struyve K. (Non)-completeness of ℝ-buildings and fixed point theorems. GROUPS GEOMETRY AND DYNAMICS. 2011;5(1):177–88.
IEEE
[1]
K. Struyve, “(Non)-completeness of ℝ-buildings and fixed point theorems,” GROUPS GEOMETRY AND DYNAMICS, vol. 5, no. 1, pp. 177–188, 2011.
@article{5644992,
  abstract     = {{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.}},
  author       = {{Struyve, Koen}},
  issn         = {{1661-7207}},
  journal      = {{GROUPS GEOMETRY AND DYNAMICS}},
  keywords     = {{metric completeness,POLYGONS,Euclidean buildings,fixed point theorems}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{177--188}},
  title        = {{(Non)-completeness of ℝ-buildings and fixed point theorems}},
  url          = {{http://doi.org/10.4171/GGD/121}},
  volume       = {{5}},
  year         = {{2011}},
}
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