arXiv subjects
Publications and source records attributed to A. Felikson.
Let $G$ be a discrete group generated by reflections in hyperbolic or Euclidean space, and $H\subset G$ be a finite index subgroup generated by reflections. Suppose that the fundamental chamber of $G$ is a finite volume polytope with $k$ facets. In this paper, we prove that the fundamental chamber of $H$ has at least $k$ facets.
Let $P$ be a simplex in $S^n$ and $G_P$ be a group generated by the reflections with respect to the facets of $P$. We are interested in the case when the group $G_P$ is discrete. In this case we say that $G$ generates the discrete reflection group $G_P$. We develop the criteria for a simplex generating a discrete reflection group. We also describe all indecomposable spherical simplices generating discrete reflection groups.
Coxeter decompositions of hyperbolic simplices where studied in math.MG/0212010 and math.MG/0210067. In this paper we use the methods of these works to classify Coxeter decompositions of bounded convex pyramids and triangular prisms in the hyperbolic space H^3.
We classify Coxeter decompositions of hyperbolic tetrahedra, i.e. simplices in the hyperbolic space H^3. The paper completes the classification of Coxeter decompositions of hyperbolic simplices.
Let X be a space of constant curvature and P be a convex polyhedron in X. A Coxeter decomposition of the polyhedron P is a decomposition of P into finitely many Coxeter polyhedra, such that any two polyhedra having a common facet are symmetric with respect to this facet. In this paper we classify Coxeter decompositions of simplices in hyperbolic space of dimension greater than 3. The problem is close to the classification of the finite index subgroups in the discrete hyperbolic reflection groups.