Abstract
This chapter presents an approach formulating axiomatization of homology and cohomology theories which makes the subject algebraic topology elegant and provides a quick access to further study. These axioms, now called Eilenberg and Steenrod axioms for homology and cohomology theories, were announced by S. Eilenberg (1915–1998) and N. Steenrod (1910–1971) in 1945 but first appeared in their celebrated book “The Foundations of Algebraic Topology” in 1952.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Adams, J.F.: Algebraic Topology: A student’s Guide. Cambridge University Press, Cambridge (1972)
Dieudonné, J.: A History of Algebraic and Differential Topology, 1900–1960. Modern Birkhäuser Classics. Birkhäuser, Basel (1989)
Eilenberg, S., Steenrod, N.: Foundations of Algebraic Topology. Princeton University Press, Princeton (1952)
Gray, B.: Homotopy Theory: An Introduction to Algebraic Topology. Academic, New York (1975)
Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)
Hilton, P.J., Wylie, S.: Homology Theory. Cambridge University Press, Cambridge (1960)
Hu, S.T.: Homology Theory. Holden Day, Oakland (1966)
Maunder, C.R.F.: Algebraic Topology. Van Nostrand Reinhold, London (1970)
Rotman, J.J.: An Introduction to Algebraic Topology, Springer, New York, 1988
Spanier, E.: Algebraic Topology. McGraw-Hill, 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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer India
About this chapter
Cite this chapter
Adhikari, M.R. (2016). Eilenberg–Steenrod Axioms for Homology and Cohomology Theories. In: Basic Algebraic Topology and its Applications. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2843-1_12
Download citation
DOI: https://doi.org/10.1007/978-81-322-2843-1_12
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2841-7
Online ISBN: 978-81-322-2843-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)