Zachery Wall

Topologists are interested in the properties of spaces preserved under homeomorphisms. These properties are called topological invariants and can be used to distinguish non-homeomorphic spaces from one another. In this talk, we will introduce a particularly significant topological invariant, called the fundamental group. To calculate the fundamental group of the circle S¹, we introduce covering maps. We explore the interplay between fundamental groups, covering maps, and lifts into the covering space. Finally, a few central results in covering space theory will be explored, including the classification theorem of coverings.