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Covering Spaces

In: Basic Algebraic Topology and its Applications

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  • Mahima Ranjan Adhikari

    (Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC))

Abstract

This chapter continues the study of the fundamental groups and is designed to utilize the power of the fundamental groups through a study of covering spaces. The fundamental groups are deeply connected with covering spaces. Algebraic features of the fundamental groups are expressed by the geometric language of covering spaces. Main interest in the study of this chapter is to establish an exact correspondence between the various connected covering spaces of a given base space B and subgroups of its fundamental group $$\pi _1(B)$$ , like Galois theory, with its correspondence between field extensions and subgroups of Galois groups, which is an amazing result.

Suggested Citation

  • Mahima Ranjan Adhikari, 2016. "Covering Spaces," Springer Books, in: Basic Algebraic Topology and its Applications, chapter 0, pages 147-196, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-2843-1_4
    DOI: 10.1007/978-81-322-2843-1_4
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