For symplectic group actions which are not Hamiltonian there are two ways to define reduction. Firstly using the cylinder-valued momentum map and secondly lifting the action to any Hamiltonian cover (such as the universal cover), and then performing symplectic reduction in the usual way. We show that provided the action is free and proper, and the Hamiltonian holonomy associated to the action i...

Let U, g, k and A be positive integers with u :::: k. A (k, A)-grOUp divisible covering design ((k, A)-GDCD) with type gU is a A-cover of pairs by k-tuples of a gu-set X with u holes of size g, which are disjoint and spanning. The covering number, C(k, A; gil), is the minimum number of blocks in a (k, A)-GDCD of type gUo In this paper, the detennination ofllie fimction C(3, A; gil) begun by [6]...

These notes, from a first course in algebraic topology, introduce the fundamental group and the fundamental groupoid of a topological space and use them to classify covering spaces.

In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of $mathbb{Z}_{m}*mathbb{Z}_{n}$ is free of rank $(m-1)(n-1)$ fo...