7 research outputs found
On manifolds with nonhomogeneous factors
We present simple examples of finite-dimensional connected homogeneous spaces
(they are actually topological manifolds) with nonhomogeneous and nonrigid
factors. In particular, we give an elementary solution of an old problem in
general topology concerning homogeneous spaces
On a Generalization of Zaslavsky's Theorem for Hyperplane Arrangements
We define arrangements of codimension-1 submanifolds in a smooth manifold
which generalize arrangements of hyperplanes. When these submanifolds are
removed the manifold breaks up into regions, each of which is homeomorphic to
an open disc. The aim of this paper is to derive formulas that count the number
of regions formed by such an arrangement. We achieve this aim by generalizing
Zaslavsky's theorem to this setting. We show that this number is determined by
the combinatorics of the intersections of these submanifolds.Comment: version 3: The title had a typo in v2 which is now fixed. Will appear
in Annals of Combinatorics. Version. 2: 19 pages, major revision in terms of
style and language, some results improved, contact information updated, final
versio