Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Combinatorial and group-theoretic compactifications of buildings
View through CrossRef
Let
X
be a building of arbitrary type. A compactification
????
sph
(
X
)
of the set
Res
sph
(
X
)
of spherical residues of
X
is introduced. We prove that it coincides with the horofunction compactification of
Res
sph
(
X
)
endowed with a natural combinatorial distance which we call the
root-distance
. Points of
????
sph
(
X
)
admit amenable stabilisers in
Aut
(
X
)
and conversely, any amenable subgroup virtually fixes a point in
????
sph
(
X
)
. In addition, it is shown that, provided
Aut
(
X
)
is transitive enough, this compactification also coincides with the group-theoretic compactification constructed using the Chabauty topology on closed subgroups of
Aut
(
X
)
. This generalises to arbitrary buildings results established by Y. Guivarc’h and B. Rémy [20] in the Bruhat–Tits case.
Title: Combinatorial and group-theoretic compactifications of buildings
Description:
Let
X
be a building of arbitrary type.
A compactification
????
sph
(
X
)
of the set
Res
sph
(
X
)
of spherical residues of
X
is introduced.
We prove that it coincides with the horofunction compactification of
Res
sph
(
X
)
endowed with a natural combinatorial distance which we call the
root-distance
.
Points of
????
sph
(
X
)
admit amenable stabilisers in
Aut
(
X
)
and conversely, any amenable subgroup virtually fixes a point in
????
sph
(
X
)
.
In addition, it is shown that, provided
Aut
(
X
)
is transitive enough, this compactification also coincides with the group-theoretic compactification constructed using the Chabauty topology on closed subgroups of
Aut
(
X
)
.
This generalises to arbitrary buildings results established by Y.
Guivarc’h and B.
Rémy [20] in the Bruhat–Tits case.
Related Results
Młodociani sprawcy przestępstw przeciwko mieniu
Młodociani sprawcy przestępstw przeciwko mieniu
The new Polish penal legislation of 1969 introduced special rules of criminal liability of young adult offenders' aged 17-20. In 1972 criminological research was undertaken in orde...
Compactifications de variétés de Siegel aux places de mauvaise réduction
Compactifications de variétés de Siegel aux places de mauvaise réduction
Dans cette thèse, nous construisons des compactifications des variétés modulaires de Siegel en leurs places de mauvaise réduction de type parahorique. Nous construisons tout d'abor...
Analytic constructions of compactifications of Bruhat-Tits buildings
Analytic constructions of compactifications of Bruhat-Tits buildings
Compactifications analytiques d'immeubles de Bruhat-Tits
Dans cette thèse, on s’intéresse aux immeubles de Bruhat-Tits et leurs compactifications. Précisément, on c...
Non-Geometric Compactifications and String Cosmology in the Swampland
Non-Geometric Compactifications and String Cosmology in the Swampland
This thesis comprises three research projects conducted during the author's doctoral program, which are presented individually in the following chapters.
In Chapter II, we demonstr...
Comparative assessment of environmental and post- occupancy evaluation of green buildings vs conventional buildings
Comparative assessment of environmental and post- occupancy evaluation of green buildings vs conventional buildings
Due to increasing office space demand and rising rental rates, stakeholders seek cost-effective alternatives that align with sustainability goals. Therefore, green building offers ...
Morphological constraints on cerebellar granule cell combinatorial diversity
Morphological constraints on cerebellar granule cell combinatorial diversity
Abstract
Combinatorial expansion by the cerebellar granule cell layer (GCL) is fundamental to theories of cerebellar contributions to motor control and learning. Gr...
Assessing energy rating premiums in the performance of green office buildings in Australia
Assessing energy rating premiums in the performance of green office buildings in Australia
Purpose– Green office buildings have recently taken on increased significance in institutional property portfolios in Australia and globally. The key issue from an institutional in...
Gravitational couplings in $$ \mathcal{N}=2 $$ string compactifications and Mathieu Moonshine
Gravitational couplings in $$ \mathcal{N}=2 $$ string compactifications and Mathieu Moonshine
Abstract
We evaluate the low energy gravitational couplings, F
g in the heterotic E
8 ×E
8 string theory compactified on or...