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Ends and Compactifications in Geometric Topology

In: Essays on Topology

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  • Ken’ichi Ohshika

    (Gakushuin University, Department of Mathematics, Faculty of Science)

Abstract

This chapter is a survey on ends and compactification of topological spaces and on their applications in manifold topology. Starting from the basic notion and properties of ends, which were first introduced by Freudenthal, we look at how it was used to deepen understanding of open manifolds. We put a particular emphasis on problems of finding open contractible manifolds different from Euclidean spaces and of attaching boundaries to open 3-manifolds. We also touch upon the special case of hyperbolic 3-manifolds with finitely generated fundamental groups, and explain how such manifolds can be compactified by attaching boundaries.

Suggested Citation

  • Ken’ichi Ohshika, 2025. "Ends and Compactifications in Geometric Topology," Springer Books, in: Louis Funar & Athanase Papadopoulos (ed.), Essays on Topology, chapter 0, pages 89-110, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-81414-3_7
    DOI: 10.1007/978-3-031-81414-3_7
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