The Center Conjecture for spherical buildings of types F4 and E6

Mathematics – Metric Geometry

Scientific paper

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34 pages. An intrinsic version of the results has been added. Proof of the Center Conjecture for spherical buildings of classi

Scientific paper

10.1007/s00039-011-0118-7

We prove that a convex subcomplex of a spherical building of type F4 or E6 is
a subbuilding or the automorphisms of the subcomplex fix a point on it. Our
approach is differential-geometric and based on the theory of metric spaces
with curvature bounded above. We use these techniques also to give another
proof of the same result for the spherical buildings of classical type.

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