TY - JOUR
T1 - The cone topology on masures
T2 - With an appendix by auguste hébert (université de lyon)
AU - Ciobotaru, Corina
AU - Mühlherr, Bernhard
AU - Rousseau, Guy
N1 - Funding Information:
Funding : C.C. was partially supported by Swiss National Science Foundation Grant 153599. Auguste Hébert was partially supported by ANR grant ANR-15-CE40-0012.
Publisher Copyright:
© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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 Δas well as on the building at infinity of Δ, 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 Δ. Under some hypotheses, with respect to the masure and the group action of G, we prove that G acts strongly transitively on Δif and only if it acts strongly transitively on the twin building at infinity a, Δ. 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.
AB - 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 Δas well as on the building at infinity of Δ, 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 Δ. Under some hypotheses, with respect to the masure and the group action of G, we prove that G acts strongly transitively on Δif and only if it acts strongly transitively on the twin building at infinity a, Δ. 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.
KW - Bruhat-Tits building
KW - Kac-Moody group
KW - Twin building
UR - http://www.scopus.com/inward/record.url?scp=85078720686&partnerID=8YFLogxK
U2 - 10.1515/advgeom-2019-0020
DO - 10.1515/advgeom-2019-0020
M3 - Journal article
AN - SCOPUS:85078720686
SN - 1615-715X
VL - 20
SP - 1
EP - 28
JO - Advances in Geometry
JF - Advances in Geometry
IS - 1
ER -