Examples of buildings constructed via covering spaces

Examples of buildings constructed via covering spaces

The purpose of this note is to use covering space theory to construct new examples of buildings. On the level of Coxeter systems, this contsruction was described previously in Davis [4]. It goes as follows. Start with a Coxeter system (W ′, S). Change some m(s, t)’s in its Coxeter matrix from integers ≥ 2 to the symbol ∞ . This defines a new Coxeter system (W, S). Suppose C′ is a building of ty...

Covering Spaces

Theory of Covering Spaces

Introduction. In this paper I study covering spaces in which the base space is an arbitrary topological space. No use is made of arcs and no assumptions of a global or local nature are required. In consequence, the fundamental group ir(X, Xo) which we obtain frequently reflects local properties which are missed by the usual arcwise group iri(X, Xo). We obtain a perfect Galois theory of covering...

Examples of function spaces

1. Non-Banach limits C(R), C∞(R) of Banach spaces C[a, b] 2. Banach completion C o (R) of C c (R) 3. Rapid-decay functions, Schwartz functions 4. Non-Fréchet colimit C∞ c (R) of Fréchet spaces 5. LF-spaces of moderate-growth functions 6. Strong operator topology 7. Generalized functions (distributions) on R 8. Tempered distributions and Fourier transforms on R 9. Test functions and Paley-Wiener...

On Holonomy Covering Spaces

Introduction. In [l] L. Markus and the author introduced the concept of holonomy covering spaces for flat affinely connected manifolds or what are also called locally affine spaces. We also proved in [l ] that the holonomy covering space of a complete « dimensional locally affine space must be some « dimensional cylinder, i.e., T^XF"-*, i = 0, •■-,«, where T* denotes the locally affine i dimens...