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On the local structure and the homology of CAT(κ) spaces and euclidean buildings
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Linus Kramer
Published/Copyright:
April 8, 2011
Abstract
We prove that every open subset of a euclidean building is a finite-dimensional absolute neighborhood retract. This implies in particular that such a set has the homotopy type of a finite dimensional simplicial complex. We also include a proof for the rigidity of homeomorphisms of euclidean buildings. A key step in our approach to this result is the following: the space of directions ∑oX of a CAT(κ) space X is homotopy equivalent to a small punctured disk Bɛ(X, o) – o. The second ingredient is the local homology sheaf of X. Along the way, we prove some results about the local structure of CAT(κ)-spaces which may be of independent interest.
Received: 2010-09-09
Revised: 2010-09-24
Published Online: 2011-04-08
Published in Print: 2011-April
© de Gruyter 2011
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Articles in the same Issue
- On finite subgroups of compact Lie groups and fundamental groups of Riemannian manifolds
- Sets resilient to erosion
- On duality and endomorphisms of lattices of closed convex sets
- On the complexity group of stable curves
- Isoperimetric inequalities for wave fronts and a generalization of Menzin's conjecture for bicycle monodromy on surfaces of constant curvature
- Character tables of m-flat association schemes
- Character tables of the association schemes obtained from the finite affine classical groups acting on the sets of maximal totally isotropic flats
- Bounds on the roots of the Steiner polynomial
- Polarities of Schellhammer planes
- Substituting compact disks in stable planes
- On the local structure and the homology of CAT(κ) spaces and euclidean buildings
- Sixteen-dimensional locally compact translation planes with collineation groups of dimension at least 38
