Covering Spaces

  • Mahima Ranjan Adhikari


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.


Conjugacy Class Fundamental Group Base Space Orbit Space Algebraic Topology 
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  1. Aguilar, M., Gliter, S., Prieto, C.: Algebraic Topology from a Homotopical View Point. Springer, New York (2002)Google Scholar
  2. Arkowitz, M.: Introduction to Homotopy Theory. Springer, New York (2011)Google Scholar
  3. Armstrong, M. A.: Basic Topology. Springer, New York (1983)Google Scholar
  4. Bredon, G.E.: Topology and Geometry. Springer, New York, Inc (1993)Google Scholar
  5. Croom, F.H.: Basic Concepts of Algebraic Topology. Springer, New York (1978)Google Scholar
  6. Davis, J.F., Kirk, P.: Lecture Notes in Algebraic Topology, Indiana University, Bloomington, IN.
  7. Dieudonné, J.: A History of Algebraic and Differential Topology, 1900–1960. Modern Birkhäuser, Boston (1989)Google Scholar
  8. Dodson, C.T.J., Parker, P.E.: A User’s Guide to Algebraic Topology. Kluwer, Dordrecht (1997)Google Scholar
  9. Dugundji, J.: Topology. Allyn & Bacon, Newtown (1966)Google Scholar
  10. Gray, B.: Homotopy Theory, An Introduction to Algebraic Topology. Acamedic Press, New York (1975)Google Scholar
  11. Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)Google Scholar
  12. Hilton, P.J.: An introduction to Homotopy Theory. Cambridge University Press, Cambridge (1983)Google Scholar
  13. Hu, S.T.: Homotopy Theory. Academic Press, New York (1959)Google Scholar
  14. Hurewicz, W.: On the concept of fibre space. Proc. Natl. Acad. Sci., USA 41, 956–961 (1955)Google Scholar
  15. Mayer, J.: Algebraic Topology. Prentice-Hall, New Jersy (1972)Google Scholar
  16. Massey, W.S.: A Basic Course in Algebraic Topology. Springer, New York (1991)Google Scholar
  17. Maunder, C.R.F.: Algebraic Topology. Van Nostrand Reinhhold, London (1970)Google Scholar
  18. Munkres, J.R.: Topology, A First Course. Prentice-Hall, New Jersey (1975)Google Scholar
  19. Munkres, J.R.: Elements of Algebraic Topology. Addison-Wesley-Publishing Company, Menlo Park (1984)Google Scholar
  20. Rotman, J.J.: An Introduction to Algebraic Topology. Springer, New York (1988)Google Scholar
  21. Spanier, E.: Algebraic Topology. McGraw-Hill Book Company, New York (1966)Google Scholar
  22. Steenrod, N.: The Topology of Fibre Bundles. Prentice University Press, Prentice (1951)Google Scholar
  23. Switzer, R.M.: Algebraic Topology-Homotopy and Homology. Springer, Berlin (1975)Google Scholar
  24. Wallace, A.H.: Algebraic Topology. Benjamin, New York (1980)Google Scholar
  25. Whitehead, G.W.: Elements of Homotopy Theory. Springer, New York (1978)Google Scholar

Copyright information

© Springer India 2016

Authors and Affiliations

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

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