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Flag-homogeneous compact connected polygons
The flag-homogeneous compact connected polygons with equal topological parametersp = q are classified explicitly. These polygons turn out to be Moufang polygons.
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The topology of a semisimple Lie group is essentially unique
We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locallyExpand
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Two-transitive Lie groups
Using a characterization of parabolics in reductive Lie groups due to Furstenberg, elementary properties of buildings, and some algebraic topology, we give a new proof of Tits' classification ofExpand
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Compact Polygons
We develop the basic topological properties of compact polygons, i.e. of compact topological Tits buildings of rank two. It is proved that the Coxeter diagram of such a building is alwaysExpand
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Flag-Homogeneous Compact Connected Polygons II
All flag-homogeneous compact connected polygons are classified explicitly. It turns out that these polygons are precisely the compact connected Moufang polygons.
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HOMOGENEOUS COMPACT GEOMETRIES
We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply ourExpand
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Simple groups of finite morley rank and Tits buildings
Theorem A:If ℬ is an infinite Moufang polygon of finite Morley rank, then ℬ is either the projective plane, the symplectic quadrangle, or the split Cayley hexagon over some algebraically closedExpand
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Transitive actions of locally compact groups on locally contractible spaces
Suppose that $X=G/K$ is the quotient of a locally compact group by a closed subgroup. If $X$ is locally contractible and connected, we prove that $X$ is a manifold. If the $G$-action is faithful,Expand
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Loop Groups and Twin Buildings
In these notes we describe some buildings related to complex Kac–Moody groups. First we describe the spherical building of SLn(ℂ) (i.e. the projective geometry PG(ℂn)) and its VeroneseExpand
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Asymptotic cones of finitely presented groups
Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S)⩾2 and let Γ be a uniform lattice in G. (a) If CH holds, then Γ has a unique asymptoticExpand
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