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Groups and symmetry
Contents: Symmetries of the Tetrahedron.- Axioms.- Numbers.- Dihedral Groups.- Subgroups and Generators.- Permutations.- Isomorphisms.- Plato's Solids and Cayley's Theorem.- Matrix Groups.-
The fundamental group of the orbit space of a discontinuous group
A group G of homeomorphisms of a topological space X will be called discontinuous if (1) the stabilizer of each point of X is finite, and (2) each point x ∈ X ; has a neighbourhood U such that any
Calculating the fundamental group of an orbit space
Suppose G acts effectively as a group of homeomorphisms of the connected, locally path connected, simply connected, locally compact metric space X. Let G denote the closure of G in Homeo^), and N the
Collars and concordances of topological manifolds
Let F : M x [0, 1-]~Ex [0, 1] be a concordance of a compact topological mmanifold in Euclidean q-space. It will be shown that there is an ambient isotopy H of E • [0, 1], fixed on E • 0, such that
A presentation for a group of automorphisms of a simplicial complex
The Bass–Serre theorem supplies generators and relations for a group of automorphisms of a tree. Recently K. S. Brown [2] has extended the result to produce a presentation for a group of