Geometry of Simplicial Complexes and Fundamental Groups of Polyhedra

  • Mahima Ranjan Adhikari


This chapter conveys the geometry of finite simplicial complexes which provides a convenient way to study manifolds and builds up interesting topological spaces called polyhedra from these complexes followed by a study of their homotopy properties with computing their fundamental groups and develops certain analytical geometric tools for subsequent chapters.


Topological Space Fundamental Group Simplicial Complex Homology Group Algebraic Topology 
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  1. Alexander, J.W.: A proof of the invariance of certain constants of analysis situs. Trans. Amer. Math. Soc. 16, 148–154 (1915)MathSciNetCrossRefMATHGoogle Scholar
  2. Armstrong, M.A.: Basic Topology. Springer, New York (1983)Google Scholar
  3. Croom, F.H.: Basic Concepts of Algebraic Topology. Springer, New York (1978)CrossRefMATHGoogle Scholar
  4. Eilenberg, S., Steenrod, N.: Foundations of Algebraic Topology. Princeton University Press, Princeton (1952)CrossRefMATHGoogle Scholar
  5. Gray, B.: Homotopy Theory: An Introduction to Algebraic Topology. Academic, New York (1975)MATHGoogle Scholar
  6. Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)MATHGoogle Scholar
  7. Hilton, P.J., Wylie, S.: Homology Theory. Cambridge University Press, Cambridge (1960)CrossRefMATHGoogle Scholar
  8. Lahiri, B.K.: First Course In Algebraic Topology. Narosa Publishing House, New Delhi (2005)MATHGoogle Scholar
  9. Maunder, C.R.F.: Algebraic Topology. Van Nostrand Reinhold, London (1970)MATHGoogle Scholar
  10. Rotman, J.J.: An Introduction to Algebraic Topology. Springer, New York (1988)CrossRefMATHGoogle Scholar
  11. Singer, I.M., Thrope, J.A.: Lecture Notes on Elementary Topology and Geometry. Springer, New York (1967)Google Scholar
  12. Spanier, E.: Algebraic Topology. McGraw-Hill Book Company, New York (1966)MATHGoogle Scholar
  13. Switzer, R.M.: Algebraic Topology-Homotopy and Homology. Springer, Berlin (1975)CrossRefMATHGoogle Scholar
  14. Veblen, O.: Analysis Situs, vol. 2. Part II. American Mathematical Society Colloquium Publications, New York (1922)Google Scholar
  15. Wallace, A.H.: Algebraic Topology. Benjamin, New York (1980)Google Scholar
  16. Whitehead, G.W.: Elements of Homotopy Theory. Springer, New York (1978)CrossRefMATHGoogle Scholar
  17. Zeeman, E.C.: Relative simplicial approximation. Proc. Camb. Phil. Soc. 60, 39–43 (1964)MathSciNetCrossRefMATHGoogle 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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