# The cone topology on masures

Abstract : Masures are generalizations of Bruhat–Tits buildings and the main examples are associated with almost split Kac–Moody groups G over non-Archimedean local fields. In this case, G acts strongly transitively on its corresponding masure ∆ as well as on the building at infinity of ∆, which is the twin building associated with G. The aim of this article is twofold: firstly, to introduce and study the cone topology on the twin building at infinity of a masure. It turns out that this topology has various favorable properties that are required in the literature as axioms for a topological twin building. Secondly, by making use of the cone topology, we study strongly transitive actions of a group G on a masure ∆. Under some hypotheses, with respect to the masure and the group action of G, we prove that G acts strongly transitively on ∆ if and only if it acts strongly transitively on the twin building at infinity ∂∆. Along the way a criterion for strong transitivity is given and the existence and good dynamical properties of strongly regular hyperbolic automorphisms of the masure are proven.
Keywords :
Document type :
Preprints, Working Papers, ...
This preprint improves the essential results in the preprint Strongly transitive actions on aff.. 2017
Domain :

Cited literature [9 references]

https://hal.archives-ouvertes.fr/hal-01479708
Contributor : Guy Rousseau <>
Submitted on : Monday, June 11, 2018 - 9:36:03 PM
Last modification on : Friday, October 26, 2018 - 10:46:20 AM
Document(s) archivé(s) le : Thursday, September 13, 2018 - 12:11:16 AM

### Files

CMRH18-11-06-18.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01479708, version 2
• ARXIV : 1703.00318

### Citation

Corina Ciobotaru, Bernhard Mühlherr, Guy Rousseau, Auguste Hébert. The cone topology on masures. This preprint improves the essential results in the preprint Strongly transitive actions on aff.. 2017. 〈hal-01479708v2〉

Record views