Abstract
This chapter continues the study of homotopy theory though the concept of fundamental groups invented by H.Poincaré (1854–1912) in 1895, which conveys the first transition from topology to algebra by assigning a group structure on the set of relative homotopy classes of loops in a functorial way.
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Adhikari, M.R., Adhikari, A.: Basic Modern Algebra with Applications. Springer, New Delhi (2014)
Aguilar, M., Gitler, S., Prieto, C.: Algebraic Topology from a Homotopical View Point. Springer, New York (2002)
Arkowitz, M.: Introduction to Homotopy Theory. Springer, New York (2011)
Armstrong, M.A.: Basic Topology. Springer, New York (1983)
Bredon, G.: Topology and Geometry. Springer, GTM 139 (1993)
Chatterjee, B.C., Ganguly, S., Adhikari, M.R.: A Textbook of Topology. Asian Books Pvt. Ltd., New Delhi (2002)
Croom, F.H.: Basic Concepts of Algebraic Topology. Springer, New York (1978)
Crowell, R.H., Fox, R.H.: Introduction to Knot Theory. Ginn and Company, Boston (1963)
Dieudonné, J.: A History of Algebraic and Differential Topology, 1900–1960. Modern Birkhäuser, Basel (1989)
Dugundji, J.: Topology. Allyn & Bacon, Newtown (1966)
Eilenberg, S., Steenrod, N.: Foundations of Algebraic Topology. Princeton University Press, Princeton (1952)
Gray, B.: Homotopy Theory, An Introduction to Algebraic Topology. Acamedic Press, New York (1975)
Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)
Hilton, P.J.: An Introduction to Homotopy Theory. Cambridge University Press, Cambridge (1983)
Hu, S.T.: Homotopy Theory. Academic Press, New York (1959)
Massey, W.S.: A Basic Course in Algebraic Topology. Springer, New York (1991)
Maunder, C.R.F.: Algebraic Topology. Van Nostrand Reinhhold, London (1970)
Munkres, J.R., Topology, A First Course. Prentice-Hall, New Jersey (1975)
Rotman, J.J.: An Introduction to Algebraic Topology. Springer, New York (1988)
Spanier, E.: Algebraic Topology. McGraw-Hill Book Company, New York (1966)
Switzer, R.M.: Algebraic Topology-Homotopy and Homology. Springer, Berlin (1975)
Whitehead, G.W.: Elements of Homotopy Theory. Springer, New York (1978)
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Adhikari, M.R. (2016). The Fundamental Groups. In: Basic Algebraic Topology and its Applications. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2843-1_3
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DOI: https://doi.org/10.1007/978-81-322-2843-1_3
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