The principal investigator will continue his studies of Kleinian groups, 3-dimensional geometry and topology, and discontinuous groups. A special investigation will be conducted into Mobius structures, geodesic laminations, lattices on trees, surface symmetries, and certain fundamental domains. The project will encompass mathematical techniques from group theory as well as a number of more standard geometric techniques. A group is an abstract mathematical object. The integers are an example of a group because one can always reverse the order of addition without changing the answer, there is a zero, subtraction is always possible, and additions may be freely associated.
