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Chapter 8 Cosmic Topology

Cosmic topology can be described as the effort to determine the shape of our universe through observational techniques. In this chapter we discuss two programs of research in cosmic topology: the cosmic crystallography method and the circles-in-the-sky method. Both programs search for topology by assuming the universe is finite in volume without boundary. The chapter begins with a discussion of three-dimensional geometry and some 3-manifolds that have been given consideration as models for the shape of our universe.