One of the ancient principles for dealing with a larger calculation is to subdivide it into smaller computational tasks. In this chapter we shall investigate one application of this principle, which allows one to break down the calculation of the homology groups of a CW complex into two hopefully simpler computations of homology groups of some chain complexes. The natural question of putting the computed information together to yield the homology groups of the original complex has an elegant algebraic answer due to Eilenberg: the so-called long exact sequences.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Exact Sequences. In: Combinatorial Algebraic Topology. Algorithms and Computation in Mathematics, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71962-5_5
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DOI: https://doi.org/10.1007/978-3-540-71962-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71961-8
Online ISBN: 978-3-540-71962-5
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