chapter  9
32 Pages

Locally Isomorphic Groups

WithL. S. Pontryagin

This chapter discusses the connections in the large between groups that are locally isomorphic. The fundamental group of a topological space is one of its most important topological invariants, reflecting, as it does, topological properties of the space that are of basic interest. Covering spaces play an essential role in various branches of mathematics. Thus the Riemann surface of a multiple valued analytic function is just a covering surface of the domain of the function, except for the adjunction of poles and branch points of finite order. The construction of the universal covering employs topological apparatus: the fundamental group and the idea of a covering space. In the theory of topological groups the notion of a covering space leads to the construction of the universal covering group.